Kurikulum Prodi S1 Matematika UI rev 1 April English Dipo · 2018-04-04 · Curriculum Document, Undergraduate Study Program Mathematics, Faculty of Mathematic and Natural Sciences,

FOREWORD

We would like to extend our appreciation and gratitude to all parties involved in the successful completion of this Undergraduate Curriculum 2016-2020 for the Program of Mathematics, Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, in particular to the Mathematics Department. The 2016-2020 curriculum is the result of the revision of the 2012-2016 curriculum, which is aligned with the vision and mission of the Department, the objectives of the Study Program, and in accordance with the Higher Education Curriculum requirement set in the Indonesian National Qualification Framework (KKNI) level 6. It aims to equip students with the ability to follow the development and progress of science and technology, meet market needs, and gain intellectual maturity. The 2016-2020 curriculum is expected to produce Bachelors of Mathematics FMIPA UI who possess several competencies that can meet stakesholder needs such as academic and scientific, professional, community, and the needs of future generations. Furthermore, Bachelors of Mathematics FMIPA UI are expected to be able to take part academically and professionally on the national, regional and global levels. Finally, it is expected that the Undergraduate Curriculum 2016-2020 for the Program of Mathematics, Department of Mathematics, FMIPA UI can be useful for all related parties in the implementation of mathematics education in UI.

Depok, 30 June 2016

Head of Department of Mathematics, FMIPA UI

(Alhadi Bustamam, Ph.D.)

NIP 197209181997021001

Curriculum Document, Undergraduate Study Program Mathematics, Faculty of Mathematic and Natural Sciences, Universitas Indonesia

TASK FORCE TEAM

Person in Charge : Alhadi Bustamam

Chair : Kiki Ariyanti

Secretary : Nora Hariadi

Advisor : Anak Agung Putri Ratna

: Ariadne L. Juwono

: Widyawati

Members : 1. Bevina D. Handari

2. Dian Lestari

3. Djati Kerami

4. Hendri Murfi

5. Hengki Tasman

6. Rianti Setiadi

7. Saskya Mary Soemartojo

8. Titin Siswantining

9. Zuherman Rustam


CONTENT

FOREWORD.........................................................................................................................................1TASK FORCE TEAM..........................................................................................................................2CONTENT.............................................................................................................................................3TABLE LIST.........................................................................................................................................4FIGURE LIST.......................................................................................................................................51. INTRODUCTION.............................................................................................................................62. VISION, MISSION, AND OBJECTIVE OF UPMATH-UI..........................................................6

2.1 Vision............................................................................................................................................62.2 Mission..........................................................................................................................................62.3 Objective.......................................................................................................................................7

3. QUALIFICASSION AND GRADUATE COMPETENCE...........................................................7

4. STRUCTURE AND CURRICULUM CONTENTS…………………………………...10 4.1 Curriculum Structure...............................................................................................................104.2 Main Competence Category........................................................................................................474.3 Curriculum Detail........................................................................................................................53

5.AUTHORITY OF CURRICULUM PURPOSE AND CURRICULUM REVIEW …………..76

6. OPPORTUNITIES FOR STUDENTS TO DEVELOP THEMSELVES………………………77

7. INSTITUTION REFERENCE......................................................................................................788. REFERENCE..................................................................................................................................79


TABLE LIST

Table 1. Description of Graduate Profile ................................................................................................. 7 Table 2. General and Specific Competency ............................................................................................. 8 Table 3. Expected Learning Outcomes (ELOs) of UPMath-UI and its relation to KKNI Level 6 Sub Points ..................................................................................................................................................... 10 Table 4. Matrix I: Group and Graduate Competency Level .................................................................. 12 Table 6. Course Distribution .................................................................................................................. 47 Table 7. Competence Parameter ............................................................................................................ 47 Table 8. Curriculum Structure Based on Main Competency Category ................................................. 48 Table 9. Match Curriculum of Mathematics Study Program with IndoMS Curriculum: ...................... 52 Table 10. University Compulsary Courses ............................................................................................ 53 Table 11. Science Compulsary Courses ................................................................................................. 53 Table 12. Faculty Compulsory Courses ................................................................................................. 53 Table 13. Department Compulsory Courses .......................................................................................... 54 Tabel 14. Study Program Compulsory Courses ..................................................................................... 54 Table 15. Elective Courses .................................................................................................................... 55 Table 16. Entire Courses in 8 Semesters ............................................................................................... 56 Table 17. Silabus UPMath-UI ................................................................................................................ 59


FIGURE LIST

Figure 1. Graduates Competency Network and Profile…………………………………….. 10 Figure 2. Courses Network ................................................................................................................... 58


1. INTRODUCTION

The Department of Mathematics FMIPA UI was founded in 1961, together with the Departments of Physics, Chemistry, and Biology. In the early years of its establishment, the Department of Mathematics occupied the Salemba UI Campus at Jalan Salemba 4, Central Jakarta. Between 1961 and 1965, the Department of Mathematics had only one permanent faculty member. Lectures were conducted with the help of several non-permanent faculty members from the National Nuclear Energy Agency (BATAN) and private companies including IBM. The first generation of Mathematics undergraduate students graduated in 1969. Beginning in 1967, the number of permanent lecturers at the Department of Mathematics increased. By 2015, the Mathematics Department has 34 permanent lecturers and 1 part-time lecturer. The qualification of teaching staff varies from Masters (S2) to Ph.D. (S3), with a majority qualification of Masters. In 1987, the Department of Mathematics moving to the new location at UI Depok Campus. Currently the Department of Mathematics occupies a 4-storey building in FMIPA UI Depok Campus. Since 2008, the Department of Mathematics offers 2 degree study programs, namely Undergraduate (Bachelors/S1) Program of Mathematics UI (UPMath-UI) and Graduate (Masters/S2) Program of Mathematics. In 2015, the Department of Mathematics added a new degree study program of the Undergraduate (Bachelors/S1) Program of Statistics. This curriculum document is a document for the Undergraduate Mathematics Study Program. 2. VISION, MISSION, AND OBJECTIVE OF UPMATH-UI

2.1 Vision

§ UPMath-UI becoming a flagship institution in the field of Mathematics and its applied science that is capable of taking action globally.”

UPMath-UI vision is inline with Department of Mathematics vision, Faculty of Mathematics and Natural Sciences vision and also Universitas Indonesia vision.

2.2 Mission

To achieve this vision, DoMath-UI has determined its missions as follows:

• Educate students to be scholars who can keep up with the development of mathematics, science and technology.

• Support and develop mathematics and multidisciplinary research activities. • Provide mathematical information services that can help people in solving problems related to

mathematics, science and technology. UPMath-UI missions are inline with Department of Mathematics visions, Faculty of Mathematics

and Natural Sciences missions and also Universitas Indonesia missions.


2.3 Objective

• Produce Sarjana Sains that are capable of initiating solutions in problem solving in accordance with the rules of the scientific and academic ethics by using mathematical concepts, and being able to keep up with the development of mathematics and other related fields.

3. QUALIFICASSION AND GRADUATE COMPETENCE

Sarjana Sains of Mathematics FMIPA UI has several competencies that can meet the needs of stakesholder. Stakesholder needs consist of the needs of science, professional needs, community needs, the needs of future generations and the needs of the world of work. Profile Bachelor of Mathematics FMIPA UI Based on the competence held by sarjana sains of mathematics FMIPA UI, then the profile of graduate of Mathematics Department of FMIPA UI can be described as listed in Table 1

Table 1. Description of Graduate Profile

Graduate Profile Sarjana Sains who capable to provide solution to solve problems by using mathematical concepts in accordance with the scientific and academic ethics and be able to keep up with the development of mathematics and other related fields.


Table 0. General and Specific Competency

General Competency Specific Competency

1 Having the ability to solve problems of mathematics and their application (C4)

1. Be able to describe Mathematics basic theory, applied mathematics basic theory, algorithm, statistics, and programming basic concepts (C3)

2. Be able to implement Basic theory of Mathematics and its applied sciences, Algorithm and programming basic concept, as well as Statistics basic concept (C4)

2 Having the ability to decide which mathematical model should be used to solve the problem (C4)

1. Be able to to solve mathematical models and analyze the results obtained.(C3)

2. Be able to analyze real-world problems and model them into mathematical form. (C4)

3. Be able to identify the basis of mathematical research. (C4)

3 Having the ability to keep up the development of mathematics and its applied science on other related sciences (C5)

1. Be able to explain mathematical theory on the development of science and technology (C3)

2. Be able to identifymathematical theories on the development of science and technology (C4)

4 Having the ability to utilize appropriate information in support of mathematics(C4)

1. Be able to use information technology as supporting the field of mathematics (C3)

2. Be able to choose appropriate information technology as supporting the field of mathematics (C3)

5 Being competitive in the working world(C4)

1. Having sensitivity and concern for environmental issues, community, nation and country

2. Having an entrepreneurial spirit that is characterized by innovation and independence based on ethics

6 Having the ability for self-development in accordance with professional needs(C4)

1. Having integrity and be able to appreciate others.

2. Be able to use spoken and written language in Indonesian and English well

3. Be able to think critically, creatively, and innovatively and have the intellectual curiosity to solve problems at the individual and group level


Beside ELO’s of UPMath-UI, Universitas Indonesia has set the general University’s ELOs (MWA Decree No 09/SK/MWA-UI/2010, article 4) as follows: UI1. Having the ability to think critically and have the intellectual curiosity to solve problems,

both individually and through team work.

UI2. Having the ability to care about issues regarding the environment, community, and nation with the basis of character and ethics

UI3. Having the ability to utilize Information and Communication Technology in accordance with the related field of science

UI4. Having the ability to use Indonesian and English well to perform activities, both academic and otherwise

UI5. Having the ability to be truthful, give appreciation and provide solidarity to others and self, built through activities in the arts and sports

UI6. Having sensitivity towards entrepreneurial opportunities, as well as the ability to utilize and develop them through innovation, independence, creativity, and cooperation based on professional ethics.

The relationship between general competence and the graduate profile of Mathematics Department of FMIPA UI can be seen in Figure 1.


Figure 1. Graduates Competency Network and Profile

Having an ability to utilize

appropriate information as

support of mathematics

Having an ability to solve problem of mathematics and its application

Having an ability to decide which proper mathematic model to solve the problem

Having an ability to keeping up the development of mathematics and its applied

science on other related sciences

Being competitive in the

working world

Having an ability for self-development in

accordance with professional needs

Curriculum Document, Undergraduate Study Program Mathematics, Faculty of Mathematic and Natural Sciences, Universitas Indonesia 10

4. STRUCTURE AND CURRICULUM CONTENTS 4.1 Curriculum Structure

The curriculum structure of UPMath-UI refers to the Decree of the Minister of National Education no. 232 / U / 2000 Article 7 paragraph (2), (3), Article 8, Article 10 and Article 11 (Attachment 3), Decree of the Minister of National Education no. 45 / U / 2002 on Higher Education Core Curriculum Article 2 paragraph (1), Article 3, Article 4, Article 5, and Article 6 (Attachment 5), Decree of UI Trustee Board. 006 / SK / MWAUI / 2004 on UI Academic Curriculum (Attachment 6), National Seminar and Workshop of MIPANet which discuss about KKNI-MIPA-based curriculum from IndoMS at UI Depok on 2 December 2014 (Appendix 7). The curriculum of UPMath-UI is arranged in such a way in line with the Vision, Mission, Purpose of UPMath-UI, KKNI Level 6 like in the Table 3, the development of Science and Technology, market needs and the formation of intellectual maturity of learners. This competency is a link between the graduate profile and the outcome of this Mathematics Study Program. Therefore the curriculum of Mathematics Study Program is: a. The elaboration of the Vision, Mission, and Objectives of the Study Program to become a strong institution at the national level and recognized internationally, in the field of mathematical education and research, and its application. b. Relevant to the needs of the present and future. The curriculum is prepared by taking into account the development of science and technology and its application as well as the market needs which are input from stakesholder and alumni of Mathematics Department of FMIPA-UI. c. The demands of student intellectual maturation. Some courses prepare and shape the intellectual maturity of students from the beginning of the lecture, among others, MPKT (Integrated Personality Development Course) and some compulsory courses and electives are delivered by active learning and e-learning. Learning in these subjects will form active students independently search and organize information and collaborate with groups of tasks both in the preparation and presentation (and maintain) of their duties, and improve communication skills both oral, and information technology. d. Lecturer aspects of research and research of students' final assignment. Several courses, especially elective courses are provided by the audiences by incorporating the latest research results, both from their own teaching staff and from current journals. This kind of discussion will make the students know the latest research topic, and have stock in preparing the research. This way will enable the students to make their final assignments well. e. Relationship between courses. Interrelationship between courses is well noted, so it appears that the courses in the first / previous semester are needed to support the next course. Some of the initial courses are used as a prerequisite for the next course. General and special competence of UPMath-UI can be grouped according to stakeholder needs as shown in Table 3.


Table 2. Expected Learning Outcomes (ELOs) of UPMath-UI and its relation to KKNI Level 6

No KKNI LEVEL 6 ELOs CLAIMs

1

Ability to apply their expertise and utilize the science and technology on their field in order to solve problems and able to adapt to the situation at hand

1. Having the ability to solve problems of mathematics and their application

2. Having an ability to utilize appropriate information as support of mathematics

• Publication, including article, undergraduate thesis

• Summary in the form of journal at UI’s repository

• Paper, undergraduate thesis, project report, assignment report

2

• Mastering theoretical concept of certain scientific fields in general and partial theoretical concept of the fields mentioned in depth. Ability to formulate

• Procedural problem solving

Having the ability to decide which mathematic model should be used to solve the problem

Assignment reports Project report

3

Ability to take precise decision based on information and data analysis and being able to Give direction on choosing various alternative solutions individually or in Group

Having an ability to keeping up the development of mathematics and its applied science on other related sciences

Assignment reports Project report

4

Being responsible for their own jobs and being reliable on the working achievement of the organization

1. Being competitive in the working world

2. Having an ability for self-development in accordance with professional needs

Paper and assessment Form of MPKT


Table 3. Matrix I: Group and Graduate Competency Level

Level.

Group General Competency Specific Competency Other Competency

Basic and Personality

Having the ability for self-development in accordance with professional needs (C4)

o Having integrity and be able to appreciate others. o Be able to use spoken and written language in Indonesian

and English well o Be able to think critically, creatively, and innovatively

and have the intellectual curiosity to solve problems at the individual and group level

Being competitive in the working world (C4) o Having sensitivity and concern for environmental

issues, community, nation and country o Having an entrepreneurial spirit that is characterized by

innovation and independence based on ethics

Knowledge Having the ability to solve problems of mathematics and their application

• Be able to describe Mathematics basic theory, applied mathematics basic theory, algorithm, statistics, and programming basic concepts (C3)

• Be able to implement Basic theory of Mathematics and its applied sciences, Algorithm and programming basic concept, as well as Statistics basic concept (C4).

Having the ability to decide which mathematical model should be used to solve the problem o Be able to to solve mathematical models

and analyze the results obtained.(C3) o Be able to analyze real-world problems

and model them into mathematical form. (C4)

o Be able to identify the basis of mathematical research. (C4)

Having the ability to keep up the development of mathematics and its applied science on other related sciences o Be able to explain mathematical theory on

the development of science and technology (C3)

Having the ability for self-development in accordance with professional needs(C4).

o Be able to use spoken and written language in Indonesian and English well

o Be able to think critically, creatively, and innovatively and have the intellectual curiosity to solve problems at the individual and group level


o Be able to identify mathematical theories on the development of science and technology (C4)

Expertise at Work

Having the ability to utilize appropriate information in support of mathematics (C4)

o Be able to use information technology as supporting the field of mathematics (C3)

o Be able to choose appropriate information technology as supporting the field of mathematics (C3)

Being competitive in the working world (C4) o Be able to use information technology as supporting

the field of mathematics (C3) o Having an entrepreneurial spirit that is characterized

by innovation and independence based on ethics

Behaviour Work Having the ability to keep up the development of mathematics and its applied science on other related sciences o Be able to explain mathematical theory on

the development of science and technology (C3)

o Be able to identify mathematical theories on the development of science and technology (C4)

Being competitive in the working world (C4) o Having an entrepreneurial spirit that is characterized

by innovation and independence based on ethics

Social Life Having the ability for self-development in accordance with professional needs (C4)

o Having integrity and be able to appreciate others. Being competitive in the working world (C4)

o Having sensitivity and concern for environmental issues, community, nation and country


Table 4. Matrix II: Learning Experience University Courses (18 Credits)

No Competency Learning Experience Scope of Materials

(substance of subject and sub subject)

Media and Technology Courses Indikator Assesments

Subcompetency Activities

1 KM 1 : Having the ability for self-development in accordance with professional needs.

KK 2: Being competitive in the professional world.


2. Be able to use spoken and written language in Indonesian and English properly.

3. Be able to think critically, creatively, and innovatively and have the intellectual curiosity to solve problems at the individual and group level.

4. Having sensitivity and concern for environmental issues, community, nation and country.

Inquiry-based learning, group discussion, presentation of discussion result.

1. Religion 2. Indonesian

Whiteboard, LCD, Computer, Textbook, e-sources

1. MPK Religion (2 credits)

2. MPK Art/Sport (1 credits)

Following the UI indicator set.

Essay, assignment, presentation.

CL and PBL: group discussion, presentation of discussion result, do the given exercise individually or team works.

1. Indonesian 2. English 3. Pancasila 4. Civic 5. Quantitative

reasoning 6. Environmental,

technological and health issuesacademic

1. MPKT Science (6 credits)

2. MPKT Social and Humanities (6 credits)

3. MPK English (3 credits)

1. Be able to think critically, creatively and innovatively and have intellectual curiosity (C4).

2. Be able to solve problems individually and in team works (C4)





Media and Technology Courses Indikator Assesments


5. Having an entrepreneurial spirit that is characterized by innovation and independence based on ethics.


Science Compulsory Courses (2 Credits)

No Competency

Learning Experience Scope of Materials (substance of

subject and sub subject)

Media and Technology Courses Indicator(s) Assesments


1 PP1: Having the ability to solve problems of mathematics and their application.

PP1.1: Be able to describe mathematics basic theory, applied mathematics basic theory, algorithm, statistics, and programming basic concepts (C3).

Inquiry-based learning, discussion, presentation, do the given exercise individually or in teamwork.

Introduction to real numbers, inequalities and absolute value, single-variable functions: types and definition, graphs (cartesian, polar and parameter), operations on functions; limits: definition and theorems, continuity; derivatives: definition, geometric meaning, derivative formulae, chain rule, high-level derivatives, implicit derivatives, applications of derivatives: maximum and minimum, theorem of averages; integrals: definition, definite and undefinite integrals, basic calculus theorems, basic attributes of integrals; integration techniques: substitution techniques, partial integrals; applications of integrals: area and

LCD, computer, whiteboard.

Basic Mathematics 1 (2 credits)

1. Be able to resolve inequality and absolute value (C3).

2. Be able to describe the graph of the function of one variable (C3).

3. Be able to determine the result of operation of one variable function (C3).

4. Be able to calculate the limit, derivative, integral of the function of one variable (C3).

5. Be able to solve problems related to derivatives and integral functions of one variable (C3).

Essay, assignment, presentation, lab assignment (only for DoMath-UI).


volume of rotating objects; transcendent functions: logarithmic and exponential functions.

Faculty Compulsory Courses (8 sks)

No Competency





1 PP3: Having the ability to keep up the development of mathematics and its applied science on other related sciences.

PP3.1: Be able to explain mathematical theory on the development of science and technology (C3).

Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise individually or teamworks.

In accordance with the scope which is set by Faculty.

Whiteboard, OHP, LCD, computer, software, textbook.

Basic Physics (2 credits)

In accordance with the indicator which is set by Faculty.

Essays, assignment, presentation.




Basic Chemistry 1 (2 credits)






General Biology (2 credits)




No Competency






PP1.1. Be able to implement basic theory of mathematics and its applied sciences, algorithm and programming basic concept, as well as statistics basic concept (C4).


Probability, random variables and probability distributions, introduction of distribution, sampling distribution, statistical interference.


Statistics Method (2 credits)

1. Be able to calculate probability of a simple event and random variable (C3).

2. Be able to count probability corresponds to the distribution of the extraction or distribution approach of a statistic (C3).

3. Be able to calculate the boundaries of a confidence interval (C3).

4. Be able to apply hypothesis testing techniques (C3).


Compulsory courses/subjects at the Department level (33 credits)

No Competency Learning Experiences Scope of Materials


Media and Technology

Subjects Indicator(s) Assessments

Sub competences Activities

1 PP1: Ability to solve problems of mathematics and its applied sciences.

PP1.1: Ability to describe basic theory of mathematics and its applied science, basic concepts of algorithm and programming as well

Group discussion, presentation of discussion result, do the given exercise individually or teamworks.

Algorithm, introduction of complexity, basic programming, introduction of data structure, introduction of parallel computing.


Algorithm and Programming (3 credits)

1. Be able to describe and rewrite the algorithm in programming language (C2).

2. Be able to explain the algorithm complexity (C2).

Essay, lab/ project report, individual/ group assignment.


as basic concept of statistics (C3).


Group, subgroup, homomorphism group, quotient group, ring, subring, homomorphism ring, quotient ring, quotient field, field extension.


Algebra (4 credits)

1. Be able to explain the basic concepts of algebraic group and ring structure (C4).

2. Be able to redemonstrate proving theorems on the algebraic structure (C3).

3. Be able to define the isomorphism of 2 groups or rings (C3).

4. Be able to explain the field extension concept (C4).


PP1.2: Ability to apply basic theory of mathematics and its applied science, basic concept of algorithm and programming as well as basic concept of statistics (C3).

Inquiry-based learning, group discussion, presentation, individual/group assignments.

Real number series, introduction of function series, function sequence, improper integrals, Fourier series, Fourier integral, Fourier transform.


Basics Mathematics 3 (3 credits)

1. Be able to define the convergence for real number series by using series test (C3).

2. Be able to define the convergence for function series by using series test (C3).

3. Be able to define functions in power series expansion (C3).

4. Be able to determine the convergence for improper integral by using improper integral testing (C3).

5. Be able to operate Fourier series to approximate simple function (C3).





Media and Technology Courses Indicators Assesments


1 PP1: Ability to solve problems of mathematics and its applied sciences.

PP1.1: Ability to describe basic theory of mathematics and its applied science, basic concepts of algorithm and programming as well as basic concept of statistics (C3).


Propositional logic, predicate logic, set, set operation, function, interference rules, proof techniques (mathematical induction, direct proof, indirect proof, and number system).


Logics and Set Theory (3 credits)

1. Be able to use propositional logic and predicate logic on simple mathematical proof (C3).

2. Be able to describe the properties of set and its operation (C3).

3. Be able to use proof techniques to solve simple mathematics problems (C3).

Essay, assignments.


Linear equation system, matrix and its properties, determinant and its properties, Euclidean vector space, linear transformation on Euclidean vector space, application on the method of least squares, vector


Linear Algebra (4 credits)

1. Be able to solve SPL by using Gauss elimination or Gauss Jordan (C3).

2. Be able to calculate matrix determinant (C3).

3. Be able to apply linear algebra concept in geometry problems that involves line and plane (C3).

4. Be able to interpret linear transformation in

Essay, assignment, lab assignment (esp. DoMath-UI).






space, inner product space, linear transformation, Eigen values and Eigen vector, application on mathematics problems.

R2 and R3 spaces geometrically (C4).

5. Be able to describe general vector space concept (C4).

6. Be able to define vector coordinate toward vector space base (C3).

7. Be able to find linear transformation Matrix in Euclidean space (C3).

8. Be able to decide if matrix is orthogonally diagonalizable (C3).

PP1.2: Ability to apply basic theory of mathematics and its applied science, basic concept of algorithm and programming as well as basic concept of statistics (C3).


Invers and transcendence function (trigonometry and hyperbolic function), integral technique (integral trigonometry, rationalizing substitution, integral, rational function), indeterminate forms.


Basic Mathematics 2 (4 credits)

1. Be able to draw 2 variable function graph (C3).

2. Be able to define the operation results of two and three variable operation (C3).

Essay, assignment, presentation, lab assignment (only for Do Math-UI).

Inquiry-based learning, group discussion,

Real number system, real number

LCD, computer,

Analysis 1 (4 credits)

1. Be able to relate concept of ordered and






presentation of discussion result, do the given exercise individually or teamworks.

sequences, limit of functions, continuity of functions.

whiteboard.

completness (supremum and infimum) to prove the properties of real number set (C4).

2. Be able to prove convergence or divergence of real number sequences (C4).

3. Be able to prove the value of limit function (C4).

4. Be able to relate the concepts of limit and continuity (C4).


Algebra and sigma algebra, probability measure in a sigma algebra and its properties, random variables, function of random variables, expectation of random variables.


Introduction of Probability Theory (2 credits)

1. Be able to explain concepts of probability in depth in relation to the measure theory approach (C4).

2. Be able to explain the concepts of random variable, function of random variable, expectation of random variable (C4).


Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise individually or

Concept of probability theory and distribution, multivariate distributions, special distributions,


Mathematics Statistics 1 (4 credits)

1. Be able to determine probablity of an event and random variable, and also its conditional probability (C3).

2. Be able to identify







teamworks. distribution of random variable function.

random variable, probabiliy density function (pdf), distribution function, mathematics expectation, and moment generating function (C3).

3. Be able to determine distribution and expectation of two random variables, conditional distribution and expectation (C3).

4. Be able to determine distributions of random variables and statistics (C3).


Distribution limit, point estimation, complete statistic, Fisher information and Rao-Cramer lower limit, hypotheses testing.


Mathematics Statistics 2 (4 credits)

1. Be able to find limit distribution of a variable random by using limit distribution determination techniques (C3).

2. Be able to find point estimation of a parameter by using maximum likelihood method and moment method (C3).

3. Be able to analyze unbiasedness and






consistency of an estimator (C4).

4. Be able to find complete statistics and unbiased estimator (C3).


Solution of one variable equation, polynomial interpolation and approximation, numerical differentiation and integration, direct method to solve linear equation system, iterative method to solve linear equation system.


Numerical Method (4 credits)

1. Be able to solve one variable equation problems through numerical approach (C4).

2. Be able to solve interpolation and approximation problems through numerical approach (C4)

3. Be able to solve numerical differentiation and integration (C4)

4. Be able to solve linear equation system problems by using direct method and iterative method (C4).


2 PP2 : Having the ability to decide which mathematic model should be used to solve the

PP2.1: Be able to to solve mathematical models and analyze the results obtained (C3).

Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise

Measurement and settlement of interest mask, basic annuity and general annuity, amortization and


Finance Mathematics (4 credits)

1. Be able to explain concepts of interest and make a model of real problems that related to interest according to







problem. PP2.2: Be able to analyze real-world problems and model them into mathematical form (C4). PP2.3: Be able to identify the basis of mathematical research (C4).

individually or teamworks.

sinking fund, bonds, yield rates, term structure of interest rate.

concept of interest (C4). 2. Be able to explain

concepts of basic annuity, more general annuity, and make a model of real problems that related to annuity (C4).

3. Be able to determine the remaining debt from an amortization, make amortization schedule and sinking fund (C3).

4. Be able to anayze the financial flow and calculate the reinvestment rate (C4).

Compulsory courses/subjects at the Study Program level (59 credits)






PP1.1: Be able to implement Basic theory of mathematics and its

Group discussion, presentation of discussion result, do the given exercise individually or

Algorithm, introduction of complexity, basic programming, introduction of data


Algorithm and programming (3 credits)

1. Be able to describe and rewrite the algorithm in programming language (C2).

Essays, Lab assignment / project reports, individual/






applied sciences, algorithm and programming basic concept, as well as statistics basic concept (C4).

teamworks. structure, introduction of parallel computing.

2. Be able to explain the algorithm complexity (C2).

group assignments.


Group, subgroup, homomorphism group, quotient group, ring, subring, homomorphism ring, quotient ring, quotient field, field extension.


Algebra (4 credits)

1. Be able to explain the basic concepts of algebraic group and ring structure (C4).

2. Be able to redemonstrate proving theorems on the algebraic structure (C3).

3. Be able to define the isomorphism of 2 groups or rings (C3).

4. Be able to explain the field extension concept (C4).


PP1.2: Be able to implement basic theory of mathematics and its applied sciences, algorithm and programming basic concept, as well as statistics basic concept (C4).


Real number series, introduction of function series, function sequence, improper integrals, Fourier series, Fourier integral, Fourier transform.


Basics Mathematics 3 (3 credits)

1. Be able to define the convergence for real number series by using series test (C3).

2. Be able to define the convergence for function series by using series test (C3).

3. Be able to define functions in power

Discussion, presentation, individual/ group assignments.






series expansion (C3). 4. Be able to determine the

convergence for improper integral by using improper integral testing (C3).

5. Be able to operate Fourier series to approximate simple function (C3).


Vectors, functions with vector values and curvilinear motion, vector fields, vector differentiation, gradients, divergence, curl, line integrals, divergence theorem, Stokes’ theorem and Green’s Theorem.


Vector Calculus (2 credits)

1. Be able to calculate the speed, acceleration, curvature of the circular motion path by using a vector derivative (C3).

2. Be able to calculate the line integral and surface integral (C3).

3. Be able to use the divergence theorem, Green's theorem, Stokes's theorem to solve problems related to line integrals and surface integrals (C3).







First-order basic differential equations, Picard’s method, high-order ODEs, methods of solving high-order ODEs, Green’s function, dynamic systems, using Frobenius’ sequence to solve DEs, Laplace transformation, Bessel functions, Legendre polynomials, chaos.


Ordinary Differential Equation (4 credits)

1. Be able to find solutions to GDP problems (C3).

2. Be able to describe solution of GDP problem by using computer program (C3).

3. Be able to analyze problem solution behavior of GDP (C4).


Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise individually or teamworks, practicum in computer lab.

Combinatorial analysis, recursive relation, divide-and-conquer relation, Boolean algebra, graph theory introduction.


Discrete Mathematics (4 credits)

1. Be able to explain the property of number theory (C4).

2. Be able to solve simple combinatorial problems (C3).

3. Be able to explain the operations on Boolean algebra (C4).

4. Be able to choose the appropriate graph model to solve optimization problems (C4).

Essays, lab assignment/ project reports, individual/ group assignments.

Inquiry-based learning, Covex functions, Whiteboard, Mathematics 1. Be able to determine the






group discussion, presentation of discussion result, do the given exercise individually or teamworks.

Kharus-Kuhn-Tucker optimal condition, optimization with limitations and solutions, linear programming, integer programming, quadratic programming, numeric approach of optimization problems without limitations, linear and multidimensional searches, Newton’s method and Aarh conjugate, penalty and barrier methods.

OHP, LCD, computer, software, textbook.

Programming (4 credits)

characteristics of the optimization problem (C3).

2. Be able to choose methods to solve optimization problems (C4).

3. Be able to deduce the solution obtained (C4).

4. Be able to use software to solve mathematical programming problems (C3).


Uniform continuity, Gauges, derivatives, Riemann’s integral, function sequences.


Analysis 2 (4 credits)

1. Be able to relate the concept of continuity and uniform continuity (C4).

2. Be able to understand the concept of gauges (C2).

3. Be able to prove the properties assosiated with derivative (C4)

4. Be able to prove Riemann’s integral value (C4).

5. Be able to prove the







properties assosiated with Riemann’s integral (C4).

6. Be able to prove convergence and uniform convergence of function sequences (C4).

7. Be able to identify the characteristics of uniformly convergent function sequences (C4).


Complex numbers, analytic functions, elementary functions, mapping elementary functions, integrals, sequences, residual and pole, applications of residuals.


Complex Function (4 credits)

1. Be able to describe the result of function mapping (C4).

2. Be able to prove properties assosiated with complex number (C4).

3. Be able to prove limit value and continuity of complex function (C4).

4. Be able to identify characteristics of analytic function (C4).

5. Be able to calculate the integral of complex function (C3).

6. Be able to relate the concepts of series, residual, and pole to







calculate integral (C4). 7. Be able to use residual

and pole to solve improper integral problems (C3).


Coordinate system, geometric objects in 2D (Lines, circles, ellipses) and their intersection, 3D (lines, circles, ellipses, spheres, ellipsoids, cones, conic sections) and their cross-sections.

LCD, computer, whiteboard, geometry software.

Analytic Geometry (3 credits)

1. Be able to determine equation of geometric object in R2 (C3).

2. Be able to determine the intersection point of the intersection of geometric objects in R2 (C3).

3. Be able to determine the equation of geometric object in R3 (C3).

4. Be able to determine the intersection point of the intersection of geometric objects in R3 (C3).

5. Be able to find solution of the coordinate problems in R3 (C3).

Essay, assignment, presentation, lab assignment.

Project based learning, group discussion, presentation of discussion result, do the given exercise individually or teamworks.

Basic modeling technique; mathematical result interpretation technique.


- Mathematical Modelling (4 credits)

1. Be able to detail real issues into the math language clearly and in detail (C2).

2. Be able to determine the variables and parameters in the







matheatical model created (C3).

3. Be able to adapt existing mathematical models to real problems that have been obtained (C3).

4. Be able to analyze the model by using basic concepts of mathematics (C4).

5. Be able to represent mathematical result that have been obtained into interpretations which can be read by non-mathematical parties (C4).


Types of PDE (hyperbolic, elliptic and parabolic), analytic and numeric solutions of PDE (hyperbolic and elliptic).


Partial Differential Equation and Boundary Condition (4 credits)

1. Be able to classify the types of PDEs (C3).

2. Be able to solve PDEs (hyperbolic and elliptic types) analytically and numerically (C3).

3. Be able to analyze problem solution behaviour of PDE (C4).


Inquiry-based learning, group discussion,

Research as a means of obtaining facts,

LCD, computer,

Research Method (2

1. Be able to create research background in






presentation of discussion result, do the given exercise individually or teamworks.

types and methods of research, determining research topics, concepts of variables and systems of variables, development of hypotheses, research plans and steps, relations and nuisance variables, methods of experimentation, sources of errors and generalizations, survey methods and constructing questions in surveys, sampling methods, validity and reliability, tutorials in making reseach proposals, writing research reports.

whiteboard. credits) the form of proposal research (C4).

2. Able to document the research result in the form of research report (C4).








Students conduct research on selected topics through: proposal creation, literature study, report writing.

a.

Research as an approach to gain the truth, various method and kinds of research, concept of variable and variable systems, formulation of hypothesis, research plan and research step, relation and nuisance variables, experiment method, sources of error and generalization, survey method and construction of survey questions, sampling techniques, validity and reliability, research proposal-making practice, research report writing.

Textbook, research journal.

Undergraduate Thesis (6 credits)

1. Be able to create research background in the field of mathematics (C4).

2. Be able to document research results using scientific principles (C4).


3 PP1: Having the ability to utilize appropriate information in support of mathematics.

PP1.1: Be able to use information technology as supporting the field of mathematics (C3).

Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise individually or teamworks, computer simulation.

Matrix computation, structured data abstraction, concept of developing structured software.


Structural Computation (3 credits)

1. Be able to understand the concept of structured programming, modular programming, procedure and function, call-by-call value and call-by-reference, recursive and iterative







operation, object oriented programming (C2).

2. Be able to understand the concept of data abstraction, data structured, static data structured, dynamic data structured, class, array, pointer, linked-list, stack and queue, tree and graph (C2).

3. Be able to use efficient algorithms on application which use programming and data structured, such as: sorting and searching algorithms (C3).

4. Be able to use structured and object oriented programming language, such as: R and Phyton (C3).

PP1.2: Be able to choose appropriate information technology as supporting the field of mathematics

Inquiry-based learning, group discussion, presentation of discussion result Do the given exercise individually or teamworks, computer simulation.

Analysis algorithm: complexities, asymptotic natation, best and worst case; recurrence relations; Design algorithm: brute-force method, divide-and-conquer,


Design and Analysis Algorithm (3 credits)

1. Be able to implement efficient algorithms on mathematics problems (C3)

2. Be able to analyze efficient algorithms (C4).

Essays, Lab assignment / project reports, individual / group assignments.






(C4). greedy, dynamic programming; algorithms on graphs.

Inquiry-based learning, group discussion, presentation of discussion result, do the given exercise individually or teamworks project.

Directed and undirected graph, tree and forest, line graph, graph coloring, matrix representation of graph, cut, application of graph.


Graph Theory (3 credits)

1. Be able to explain properties of directed and undirected graph (C4).

2. Be able to prove the properties of tree and forest that have been studied (C3).

3. Be able to determine the pattern of graph coloring (C4).

4. Be able to choose appropriate graph model to solve graph application problems (C4).



Election courses/subjects at the Department level (24 credits)





1

PP1: Having the ability to utilize appropriate information in support of mathematics.

PP1.1: Be able to use information technology as supporting the field of mathematics (C3).


Approximation theory, approximation of eigenvalues, numeric solutions of nonlinear system, initial value and limit value problems for DEs.


Numerical Mathematics (3 credits)

1. Be able to explain and rewrite numeric algorithms (C2).

2. Be able to solve mathematical problems using numeric methods (C4).


PP1.2: Be able to choose appropriate information technology as supporting the field of mathematics (C4).


Initial value problems and limit value problems for ODEs, application of initial value problems and limit value problems, Brownian motion, stochastic differential equations, stochastic integrals, numeric methods for stochastic differential equations, application of stochastic differential equations.


Scientific Computation (3 credits)

1. Be able to identify initial value problems and limit value problems for ODEs (C4).

2. Be able to solve initial value problems and limit value problems for ODEs with numeric approach (C4).

3. Be able to solve application problems of initial value problems and limit value problems for ODEs (C4).

4. Be able to identify stochastic differential







equation (C4). 5. Be able to solve ODEs

with numeric approach (C4).

6. Be able to solve application problems of stochastic differential equation (C4).


Parallel computation architecture, programming concepts based on similar memory, shared and hybrid memory, related implementations of parallel programming (examples of OpenMP, MPI, CUDA, accelerated programming).


Parallel Computation (3 credits)

1. Be able to explain program parallelization seen from work side and data (C2).

2. Be able to identify part of serial program which can be parallelized (C4).

3. Be able to optimize parallel program using parallel software (C4).


2 PP2 : Having the ability to decide which mathematic model should be used to solve the problem.

PP2.1: Be able to to solve mathematical models and analyze the results obtained (C3). PP2.2: Be able to analyze real-world


Basic quantities on survival analysis: introduction, cases example and data types on survival analysis data, survival function,


Survival Analysis (3 credits)

1. Be able to understand statistical analysis technique for time-to-event data (C3).

2. Be able to explain how to treat time-to-event data for the

Essays, project reports, individual/group assignments.






problems and model them into mathematical form (C4). PP2.3: Be able to identify the basis of mathematical research (C4).

hazard function, function of mean residual life and median life, parametric models for survival data; censored and truncated: introduction, right censored, left censored or interval, truncated, likelihood construction for truncated and censored data; non-parametric estimation on right censored data and left truncated: hypothesis testing; semiparametric proportional hazard regression with fixes covariate.

purposes of analysis and modeling (C3).

3. Be able to perform various statistical analysis techniques both ini censored and truncated survival time data (C3).

Inquiry-based learning, group discussion, presentation of discussion result, do the given assignment individually or teamworks,

Calculus variation problems: Euler’s equation, transversality condition, autonomous systems, diagram analysis; optimal control

LCD, whiteboard, software, textbook, research journal.

Control Optimal Theory (3 credits)

1. Be able to determine characteristics of control optimal problems (C3).

2. Be able to choose methods for solving control optimal problems (C3).







computer lab assignment.

theory: types of endpoint applications in investment and advertisement, Pontryagin’s principle, dynamic programming, optimal stochastic control.

3. Be able to make conclusions of the solutions that have been obtained (C4).

4. Be able to use software for solving control optimal problems (C3).

Inquiry-based learning, group discussion, presentation of discussion result, do the given assignment individually or teamworks, computer lab assignment.

Theory and basic definitions of networks, design and analysis of networks, shortest-path algorithms, algorithms for minimum spanning trees, planar graphs, maximum flow and cost flow, generalization of flows problems, multicommodity flows, case studies.


Network Optimization (3 credits)

1. Be able to determine characteristics of network optimization problems (C3).

2. Be able to choose methods for solving network optimization problems (C4).

3. Be able to make conclusion of the solution that have been obtained (C4).

4. Be able to use software for solving network optimization problems (C3).


Inquiry-based learning, group discussion, presentation of discussion result, do the given assignment

Introduction to simple linear regressions, assumptions in modeling, simple linear regression

Whiteboard, OHP, LCD, computer, textbook.

Regression Analysis 1 (3 credits)

Be able to construct linear regression models and use them properly and correctly in real problems (C4).







individually or teamworks.

analysis, double linear regression analysis, modeling construction: independent variables, qualitative and quantitative variables, first order model, second order model, some regression pitfalls.

Inquiry-based learning, group discussion, presentation of discussion result, do the given assignment individually or teamworks.

Introduction, basic concept of time series, stationary, autocorrelation function, model for stationary series (ARIMA Model), model for non-stationary series, model specification, parameter estimation model, diagnostic model, forecasting, seasonal model (SARIMAModel).

Whiteboard, OHP, LCD, computer, textbook.

Time Series Analysis (3 credits)

1. Be able to explain basic concept of time series theory (C3).

2. Be able to construct models based on time series data (C4).










Metric space, topological space, continuity and homomorphism, space made out of other spaces, connectedness, compactness, axiom of separation and countability, special topics of topology (contractive mapping on metric space, linear space with norms).


Topology (3 credits)

1. Be able to prove a space is a metric space (C4).

2. Be able to prove a space is a topology space (C4).

3. Be able to explain topology space, homorphism and the connectedness (C2).

4. Be able to relate properties on topology space and prove them (C4).








Vector space as an algebraic structure, space of inner product, linear transformation, dual space, Eigen values and Eigen vectors, spectral theorems.


Linear Algebra 2 (3 credits)

1. Be able to explain the concept of general vector space as an algebraic structure (C4).

2. Be able to construct bases transformation matrix in general vector space (C3).

3. Be able to find linear transformation matrix of general vector space (C3).

4. Be able to explain the concept of dual space (C4).

5. Be able to compute Eigen values and Eigen vectors from linear transformation on general vector space (C3).



Metric space, convergence, completness properties, space with norm and its properties, linear functional, dual space, inner product space and its properties,


Functional Analysis (3 credits)

1. Be able to explain concepts in metric space, Banach space, and Hilbert space (C4).

2. Be able to identify operator in a space with norm and inner product space (C4).

3. Be able to detail the







othonormal set, functional representation in Hilbert space, some special operators, Hahn-Banach theorem and its applications, application of functional analysis in another fields.

proofs of theorems in functional analysis (C4).

4. Be able to use functional analysis concept on simple application in mathematics field (fixed point theorem) (C4).


Measured functions, measurements, integrals, integrated functions, Lebesque space (Lp), mode of convergence, measuring decomposition, generation of measures, applications of measure theory and integration in other areas of study.


Measure Theory (3 credits)

1. Be able to prove measure (C4).

2. Be able to prove a function is a measurable function (C4).

3. Be able to prove measurable space (C4).

4. Be able to explain basic concept of Lebegue integral (C2).

5. Be able to relate properties in measurable space and prove them (C4).

6. Be able to determine the relation of sequence convergent properties in measurable space







(C4).


Description of queuing problems, characteristics of queuing system, Poison process, Markov process, birth-death process, queuing systems models, Erlang model, priority queuing model, arrival pattern/ general service queuing model, characteristics of dynamic programming, muti-stage decision making, Bellman principles, one dimension dynamic programming, multi dimension dynamic programming, stochastic dynamic programming, using dynamic programming software for solving dynamic programs, real life application


Operation Research (3 credits)

1. Be able to determine characteristics and principles of dynamic programming and queuing theory (C3)

2. Be able to choose methods for solving dynamic programming and queuing problems (C3)

3. Be able to make conclusion from the obtained solution (C4)

4. Be able to use software of dynamic programming and queuing theory (C3)







of dynamic programs.

PP3.2: Be able to identify mathematical theory on the development of science and technology (C4).


Language and automata, abstract machine, computability theory.


Computation Theory (3 credits)

1. Be able to explain an abstract machine mathematically (C2).

2. Be able to explain computability theory (C3).

3. Be able to dianode language and expression language that can be accepted by an abstract machine (C4).



Depending on the given topics.


Special Topics 1 & 2 (3 credits)

1. Be able to explain basic theories that are discussed on the special topics (C3)

2. Be able to identify mathematical theories on real life problems (C4)

3. Be able to implement the theories that have been discussed for solving related problems (C3).



To complete the Mathematics Study Program of Mathematics Department of Mathematics and Natural Sciences UI, students are required to participate in academic activities with minimum weight of 144 (one hundred and four) SKS within 3.5 years and maximum of 6 years. The course that students should take in this program can be seen in Table 5.

Table 5. Course Distribution

Course Type CREDIT Total

Compulsary

University 18

120

Scinece and Engineering Group 2

Faculty 8

Department 33

Study Program 59

Elective 24 24

Total 144

4.2 Main Competence Category

Main Competence Category is a competency category that must be achieved by graduates of S1 Mathematics Study Program, based on Good Practice Book in Quality Guarantee of Higher Education, Book II on Curriculum of Study Program, Kemendiknas, 2005. Competency Parameters are coded KK1, KK2, KK3, PP1, PP2 , KM1, and KM2 shown in Table 6 and Curriculum Structure based on this category are shown in Table 7.

Table 6. Competence Parameter

Parameter Kode Kompetensi

Skill Works KK1 • Having the ability to utilize appropriate

information in support of mathematics

KK2 • Being competitive in the working world

Knwoledge

PP1 • Having the ability to solve problems of mathematics and their application

PP2 • Having the ability to decide which mathematic model should be used to solve the problem

PP3 • Having the ability to keep up the development

of mathematics and its applied science on other related sciences

Managerial Capabilities KM1 • Having the ability for self-development in accordance with professional needs


Table 7. Curriculum Structure Based on Main Competency Category

COMPETENCY OBJECTION PARAMETER EXPECTED LEARNING OUTCOMS COURSES CREDITS SMT %

MAIN Has a Strong Mathematical Basic

PP1: Having the ability to solve problems of

mathematics and their application

1. Be able to describe Mathematics basic theory, applied mathematics basic theory, algorithm, statistics, and programming basic concepts

Basic Mathematics 1 2 1

53%

Statistics Method 2 1

Logics and Set Theory 3 1

Linear Algebra 4 2

Algorithm and Programming 3 2

Algebra 4 3

2. Be able to implement Basic theory of Mathematics and its applied sciences, Algorithm and programming basic concept, as well as Statistics basic concept


Mathematics Statistics 1 4 3

Numerical Methods 4 3


Ordinary Differential Equation 4 3

Analysis 1 4 4

Introduction of Probability Theory 2 4


Mathematics Statistics 2 4 4

Discrete Mathematics 4 4

Mathematics Programming 4 4

Research Method 2 5

Vector Calculus 2 5

Analysis 2 4 5

Analytic Geometry 3 5

Mathematical Modelling 4 6

Complex Function 4 6

Partial Differential Equation and Boundary Condition

3 6

SUPPORT

Able to solve mathematical problems and applied and follow the development of science

KK1 : Having the ability to utilize appropriate information in support of mathematics

1. Be able to use information technology as supporting the field of mathematics .

Structural Computation 3 5

34%

Numerical Mathematics 3 5

2. Be able to choose appropriate information technology as supporting the field of mathematics

Design and Analysis Algorithm 3 6

Scientific Computation 3 5

Parallel Computation 3 6

PP2 : Having the ability to 1. Be able to to solve Finance Mathematics 4 6


decide which mathematic model should be used to solve the problem

mathematical models and analyze the results obtained.

2. Be able to analyze real-world problems and model them into mathematical form.

3. Be able to identify the basis of mathematical research.

Graph Theory 3 5

Survival Analysis 3 5

Regression Analysis 1 3 5

Control Optimal Theory 3 6

Network Optimization 3 6

Time Series Analysis 3 6

PP3: Having the ability to keep up the development of mathematics and its applied science on other related sciences

1. Be able to explain mathematical theory on the development of science and technology.

Basic Chemistry 1 2 1

General Biology 2 3

Basic Physics 2 4

Linear Algebra 2 3 5

Operation Research 3 5

Topology 3 6

Functional Analysis 3 7

Measure Theory 3 7

2. Be able to identify mathematical theories on the development of science and technology.

Computation Theory 3 7

Special Topics 1 3 7

Special Topics 2 3 7


Undergraduate Thesis 6 7-8

OTHER

Character, Critical Thinking, Insightful, Able to speak

KM 1 : Having the ability for self-development in accordance with professional needs KK 2: Being competitive in the working world


7. Be able to use spoken and written language in Indonesian and English with baik.in.

8. Be able to think critically, creatively, and innovatively and have the intellectual curiosity to solve problems at the individual and group level

9. Having sensitivity and concern for environmental issues, community, nation and country

10. Having an entrepreneurial spirit that is characterized by innovation and independence based on ethics

MPK Religion 2 2

13%

MPK Sport/Art 1 1

MPK English 3 1

MPKT Social and Humanities (A) 6 2

MPKT Science (B) 6 1

Note: Students must take at least 49 credits of supportive competencies, including compulsory courses of study programs.


The curriculum of Mathematics Study Program is made by referring to the results of alumni tracer study, input from lecturers and students as well as the minimal curriculum of IndoMS. Therefore there are some courses that match the minimal curriculum of IndoMS as shown in Table 8 below: Table 8. Match Curriculum of Mathematics Study Program with IndoMS Curriculum:

IndoMS Minimal Curriculum SKS Course at UpMath-UI SKS

Basics of Mathematics: logic, evidentiary method, quarters, set, relations, mapping, native, round, and rational system

3 Logics and Set Theory 3

Discrete Mathematics: combinations and permutations, pigeon hole principles, basics of graph theory

3 Discrete mathematics 4

Differential and integral calculus: the system of real numbers, functions, limits, continuity, derivatives, integral, sequence, series, vector functions, two / three variable functions, two / three fold integral, simple differential equations, introductory of numerical methods (3-4 courses)

12

Basic Mathematics 1 2



Vector Calculus 2

Fungsi Kompleks (1 – 2 mata kuliah) 4 Complex Function 4

Real Analysis (1 – 2 courses) 4

Analysis 1 4

Analysis 2 4

Linear Algebra Elementer (matrix algebra of real and complex numbers): system of linear equations, matrices, vector space, basis, linear transformation, matrix representation, inner product, orthogonalization, eigenvalues and vectors, diagonalisation and decomposition, quadraticform. (1-2 courses)

4

Linear Algebra 4

Linear Algebra 2 3

Algebra Structure: Introduction of Group and ring theory ( 1-1 courses) 4 Algebra 4

Analytic Geometry 3 Analytic Geometry 3

Numerical Methods 3 Numerical Methods 4

Algorithm and Programming 3 Algorithm and Programming 3

Ordinary Differential Equation 3 Ordinary Differential Equation 4

Partial Differential Equation 3 Partial Differential Equation and Boundary Condition 3

Mathematical Modelling 3 Mathematical Modelling 4


Linear Programming 3 Mathematics Programming 4

Statistics Method 3 Statistics Method 2

Probability Theory 3 Introduction of Probability Theory (some included in

2

Mathematics Statistics 3 Mathematics Statistics 1 4

Mathematics Statistics 2 4

Undergraduate Thesis 6 Undergraduate Thesis 6

Minimal credits/SKS 70 Total 85

4.3 Curriculum Detail

As a study program within the Mathematics Department of FMIPA UI, details of Curriculum given in this Study Program are divided into several groups, namely University Compulsory Courses, Science Compulsary Courses, Faculty Compulsory Courses, Department Compulsory Courses, each shown in Table 9 through Table 12, as well as the Compulsory Courses of the Study Program, the Mathematics Elective Courses, each of which is given in Table 13 through Table 14. The courses categorized in Table 15 are included in the curriculum details of this Study Program

.

Table 9. University Compulsary Courses

University Compulsary Courses (18 SKS)

No Code Course Credit Requirement

1 UIGE60 MPKT Science (B) 6 -

2 UIGE60 MPKT Social and Humanities (A) 6 -

3 UIGE60 MPK Religion 2 -

4 UIGE60 MPK Sport/Art 1 -

5 UIGE60 MPK English 3 -

Total 18

Table 10. Science Compulsary Courses

Science Compulsary Courses (2 SKS)


1 UIST601110 Basic Mathematics 1 2 - Total 2

Table 11. , Faculty Compulsory Courses

Faculty Compulsory Courses (8 SKS)



1 SCMA601200 Statistics Method 2 -

2 SCFI601110 Basic Physics 2 -

3 SCCH601101 Basic Chemistry 1 2 -

4 SCBI601112 General Biology 2 -

Total 8

Department Compulsory Courses and Study Program Compulsory Courses are given as a result of consideration to achieve the competencies of the expected graduates as in Table 4, namely the Main Competency Category.

Table 12. Department Compulsory Courses

Department Compulsory Courses (33 SKS) No Code Course Credit Requirement

1 SCMA601100 Logics and Set Theory 3 -

2 SCMA601111 Basic Mathematics 2 4 Basic Mathematics 1

3 SCMA601123 Linear Algebra 4 LOGICS AND SET THEORY

4 SCMA602131 Analysis 1 4 Basic Mathematics 2

5 S T602005 Introduction of Probability Theory 2 Statistika Matematika 1

6 SCMA602211 Mathematics Statistics 1 4 Statistics Method, Basic Mathematics 1

7 SCMA602212 Mathematics Statistics 2 4 Statistika Matematika 1

8

SCMA602402 Numerical Methods 4 Algorithm and Programming, Linear Algebra , Basic Mathematics 1

9 SCMA603533 Finance Mathematics 4 Basic Mathematics 2

Total 33

Tabel 13. Study Program Compulsory Courses

Study Program Compulsory Courses (59 SKS)


1 SCMA601400 Algorithm and Programming 3 Logics and Set Theory

2 SCMA602113 Basic Mathematics 3 3 Basic Mathematics 2

3 SCMA603114 Vector Calculus 2 Basic Mathematics 2

4 SCMA602122 Algebra 4 Linear Algebra

5 SCMA602151 Ordinary Differential Equation 4 Basic Mathematics 2

6 SCMA602401 Discrete Mathematics 4 Logics and Set Theory

7 SCMA602311 Mathematics Programming 4 Linear Algebra, Basic Mathematics 2

8 SCMA602403 Structural Computation 3 Algorithm and Programming, Linear Algebra

9 SCMA603441 Design and Analysis Algorithm 3 Algorithm and Programming

10 SCMA603132 Analysis 2 4 Analysis 1


11 SCMA603133 Complex Function 4 Basic Mathematics 3, Vector Calculus

12 SCMA603140 Analytic Geometry 3 Linear Algebra

13 SCMA603152 Mathematical Modelling 4 Ordinary Differential Equation, Mathematics Statistics 1

14 SCMA603153 Partial Differential Equation and Boundary Condition 3 Ordinary Differential Equation

15 SCMA603901 Research Method 2 Have got 70 credits

16 SCMA603162 Graph Theory 3 Discrete Mathematics

10 SCMA604902 Undergraduate Thesis 6 Have got 114 credits

Total 59

Elective Courses Supporting Thesis Study Program (48 SKS) includes: In addition to taking the lecture listed in the following table, students can take the Faculty Lecture Lecture (maximum 6 credits) or take a Lecture in Prodi S1 Statistics.

Table 14. Elective Courses


1 SCMA603134 Topology 3 Analysis 1

2 SCMA604123 Linear Algebra 2 3 Algebra

3 SCMA604135 Functional Analysis 3 Analysis 1and Algebra

4 SCMA604136 Measure Theory 3 Analysis 2

5 SCMA 603332 Operation Research 3 Mathematics Programming and Mathematics Statistics 2

6 SCMA603331 Network Optimization 3 Discrete Mathematics, Mathematics Programming

7 SCMA603341 Control Optimal Theory 3 Ordinary Differential Equation, Mathematics Programming

8 SCMA604412 Scientific Computation 3 Algorithm and Programming, Discrete Mathematics

9 SCMA603421 Parallel Computation 3 Algorithm and Programming

10 SCMA603431 Numerical Mathematics 3 Numerical Methods

11 SCMA603432 Computation Theory 3 Numerical Methods, Ordinary Differential Equation, Mathematics Statistics 1

12 SCST603010 Regression Analysis 1 3 Mathematics Statistics 1 and Linear Algebra

13 SCST603103 Time Series Analysis 3 Analisis Regresi I 14 SCST603201 Survival Analysis 3 Mathematics Statistics 1

15 SCMA604991 Special Topics 1 3 16 SCMA604992 Special Topics 2 3


The entire course is distributed into 8 Semesters as follows:

Table 15. Entire Courses in 8 Semesters

SEMESTER 1 SEMESTER 2 SEMESTER 3 SEMESTER 4

Code COURSES SKS Code COURSES SKS Code COURSES SKS Code COURSES SKS

Wajib

UIGE60 MPKT Science (B) 6 UIGE60 MPKT Social and Humanities (A) 6 SCBI601112 General Biology 2 SCFI601110 Basic Physics 2

UIGE60 MPK English 3 UIGE60 MPK Religion 2 SCMA602122 Algebra 4 SCMA602131 Analysis 1 4

UIGE60 MPK Sport/Art 1 SCMA601123 Linear Algebra 4 SCMA602211 Mathematics Statistics 1 4 SCST602005 Introduction of Probability Theory 2

UIST601110 Basic Mathematics 1 2 SCMA601111 Basic Mathematics 2 4 SCMA602151 Ordinary Differential Equation 4 SCMA602311 Mathematics

Programming 4

SCMA601200 Statistics Method 2 SCMA601400 Algorithm and Programming 3 SCMA602113 Basic Mathematics 3 3 SCMA602212 Mathematics Statistics 2 4

SCCH601101 Basic Chemistry 1 2 SCMA602402 Numerical Methods 4 SCMA602401 Discrete Mathematics 4

SCMA601100 LOGICS AND SET THEORY Theory 3

University Compulsary 10 University Compulsary 8 University Compulsary 0 University Compulsary 0

Science-Tech Compulsary 2 Science-Tech

Compulsary 0 Science-Tech Compulsary 0 Science-Tech

Compulsary 0

Faculty Compulsary 4 Faculty Compulsary 0 Faculty Compulsary 2 Faculty Compulsary 2

Department Compulsary 3 Department Compulsary 8 Department

Compulsary 12 Department Compulsary 6

UP Compulsary 0 UP Compulsary 3 UP Compulsary 7 UP Compulsary 12

Election 0 Election 0 Election 0 Election 0

Total SKS semester 1 19 Total SKS semester 2 19 Total SKS semester 3 21 Total SKS semester 4 20


SEMESTER 5 SEMESTER 6 SEMESTER 7 SEMESTER 8 Kode MATA KULIAH SKS Kode MATA KULIAH SKS Kode MATA KULIAH SKS Kode MATA KULIAH SKS

Wajib

SCMA603132 Analysis 2 4 SCMA603152 Mathematical Modelling 4 SCMA604902 Undergraduate Thesis 6

SCMA603162 Graph Theory 3 SCMA603153 Partial Diff.l Equation and Boundary Condition 3

SCMA603901 Research Method 2 SCMA603133 Complex Function 4

SCMA603114 Vector Calculus 2 SCMA603533 Finance Mathematics 4

SCMA603403 Structural Computation 3 SCMA603441 Design and Analysis Algorithm 3

SCMA603140 Analytic Geometry 3

Pilihan

SCMA604123 Linear Algebra 2 3 SCMA603134 Topology 3 SCMA604135 Functional Analysis 3

SCMA603332 Operation Research 3 SCMA603341 Control Optimal Theory 3 SCMA604136 Measure Theory 3

SCMA603431 Numerical Mathematics 3 SCMA603331 Network Optimization 3 SCMA604412 Computation Theory 3

SCMA603432 Scientific Computation 3 SCMA603421 Parallel Computation 3 SCMA604991 Special Topics 1 3 SCMA604991 Special Topics 1 3

SCST603201 Survival Analysis 3 SCST603010 Regression Analysis 1 3 SCMA604902 Special Topics 2 3 SCMA604902 Special Topics 2 3

SCST603103 Time Series Analysis 3

University Compulsary 0 University Compulsary 0 University Compulsary 0 University Compulsary 0

Science-Tech Compulsary 0 Science-Tech

Compulsary 0 Science-Tech Compulsary 0 Science-Tech

Compulsary 0

Faculty Compulsary 0 Faculty Compulsary 0 Faculty Compulsary 0 Faculty Compulsary 0

Department Compulsary 0 Department Compulsary 4 Department

Compulsary 0 Department Compulsary 0

UP Compulsary 17 UP Compulsary 14 UP Compulsary 6 UP Compulsary 0

Election 6 Election 3 Election 9 Election 6

Free Election 0 Free Election 0 Free Election 0 Free Election 0

Total SKS semester 5 23 Total Total 21 Total SKS semester 7 15 Total SKS semester 8 6


Figure 1. Courses Network


Table 16. SyllabusUPMath-UI

Code Courses (Credit) Requirement Genral Objective Course Content Reference

UIST601110 BASIC

MATHEMATICS 1 (2 SKS)

Explaining basic concepts in calculus

Introduction to real numbers, Inequalities and absolute value; Single-variable functions: types and definition, Graphs (Cartesian, polar and parameter), Operations on functions; Limits: Definition and theorems, Continuity; Derivatives: Definition, Geometric meaning, Derivative formulae, Chain rule, High-level derivatives, Implicit derivatives, Applications of derivatives: maximum and minimum, theorem of averages; Integrals: Definition, Definite and undefinite integrals, Basic calculus theorems, Basic attributes of integrals; Integration techniques: Substitution techniques, Partial integrals; Applications of integrals: Area and volume of rotating objects; Transcendent functions: Logarithmic and exponential functions.

• D. Varberg & E.S Purcell, 9th ed, Calculus, 2007, Prentice-Hall.

• G.B Thomas & R.L Finney, Calculus and Analytic Geometry, 9th ed, 1996, Addison-Wesley.

SCMA601100 LOGICS AND SET

THEORY (3 SKS)

Explaining basic concepts in mathematical thinking

Propositions, connecting propositions, interpretation of propositions. Valid, satisfiable and contradictory sentences. Truth tables, semantic trees, logical equivalence of two propositions, sentence schemes, predicates, universal quantification, existential quantification, interpretation of logical predicates. Translation of everyday sentences into logical predicates, logical equivalence of two sentences; rule of inference, direct proofs, indirect proofs, proof by contradiction, and mathematical induction.

• K. H. Rosen, Discrete Mathematics and Its Applications, 6thed., 2007, McGraw-Hill, Inc., International Editions.

• H. Jerome Keisler & Joel Robbin, Mathematical Logic and Computability, 1996, McGraw-Hill, Inc., International Editions.

SCMA601111 BASIC MATHEMATICS 2

UIST601110 (BASIC


Transcendent and inverse functions (trigonometric and hyperbolic functions), Integral techniques

• D. Varberg and E.S Purcell, Calculus, 9th ed, 2007,


(4 SKS) MATHEMATICS 1) (trigonometric integrals, rationalizing substitutions, integrals of rational functions), undetermined forms, parametric equality, polar coordinates, area in polar coordinates; Applications of integrals: length of curves and surface area of rotating objects; Multivariable functions: Limits, continuity, partial derivatives, differentiability, directional derivatives, tangent planes, double and triple integrals. Jacobian; row of real numbers.

Prentice-Hall. • G.B Thomas and R.L

Finney, Calculus and Analytic Geometry, 9th ed, 1996, Addison-Wesley.

SCMA601120 LINEAR

ALGEBRA (4 SKS)

SCMA601100 (LOGICS AND SET THEORY)

Explaining basic concepts in matrices, vector space and transformation

System of linear equations; determinants; two- and three-dimensional vectors; Euclidean space; general vector space; inner products; eigenvalues and eigen vectors; linear transformations; Additional topics: Application of differential equations, quadratic forms, least squares fitting, LU decomposition.

• H. Anton, Elementary Linear Algebra, 9th ed., 2005, John Wiley.

• P. R. Halmos, Finite Dimensional Vector Spaces, 1987, Springer Verlag, New York.

SCMA601200 STATISTICS

METHOD (2 SKS)

Students are expected to be able to explain statistical concepts

Probability, conditional probability; Random variables and probability distribution; Introduction to distribution: Probability distribution of random discrete variables (Binomial, Poisson and hypergeometric distributions), Probability distribution of random continuous variables (normal distribution), sampling distribution, basic limit theorems, chi-squared distribution, t distribution, F distribution; Statistical inference: Interval estimation and testing hypotheses for one and two populations; Chi-square tests; Independence tests; homogeneity tests, similarity tests, simple linear regression, ANOVA (one-way variable analysis)

• R. E. Walpole, R. H. Myers, S.L. Myers & K.Ye. Probability & Statistics for Engineers and Scientists, 7th ed, 2002, Prentice Hall International Edition.

• J. T. Mc Clave & F. H. Dietruch., Statistics, 9th ed., 2003, Prentice Hall

• R. A. Johnson, & G. K. Bhattacharyya, Statistics: Principles and Methods, 3rded., 1996, John Willey & Sons

SCMA601400

ALGORITHM AND

PROGRAMMING (3 SKS)


Students are expected to be able to explain basic concepts in algorithms and programming

Algorithms; complexity of algorithms; growth of functions; programming; conditional statements; operators, assignment and expressions; repeated structures, functions, arrays, types of data algorithms.



• Deitel and Deitel, How to Program, 7th ed., 1997, Prentice-Hall.

• B. Pfaffenberger, Computers in Your Future, 6th ed, 2002, Prentice-Hall.

SCMA602112 BASIC

MATHEMATICS 3 (3 SKS)

SCMA601111 (BASIC MATHEMATICS 2)


Series of real numbers: definition, convergence tests; Series: function series, power series, Taylor and Maclaurin series, uniform convergence; Improper integrals: definition, convergence tests, Fourier series, Fourier integrals, Fourier transformation

• W., Spiegel., Advanced Calculus, 2nd ed., Schaum’s Series, 2002, McGraw Hill

• Edward & Penney, Multivariate Calculus, 6th ed, 1998, PrenticeHall

• D. Varberg and E.S Purcell, Calculus, 9th ed, 2007, Prentice-Hall.

• E. Kreyszig, Advanced Engineering Mathematics, 8th ed, John Wiley & Sons Inc.

SCMA602122 ALGEBRA (4 SKS)

SCMA601123 (LINEAR ALGEBRA)

Explaining basic concepts in algebraic structures

Groups: normal subgroups, quotient groups, homomorphism of groups, Cayley’s theorem, Lagrange theorem, permutation of groups; ring theory: area of integrals, primary ideals, quotient rings, Euclidean rings, polynomial rings, homomorphism of rings and fields.

• J. Gallian, Contemporary Abstract Algebra, 2010, Books/Cole

• N. Herstein, Abstract Algebra, 3rd ed, 1996, Prentice Hall.

• I. N. Herstein, Topics in Algebra, 2nd, 1975, John Wiley & Sons.

SCMA602131 ANALYSIS 1 (4 SKS)


Explaining basic concepts in real number analysis

Real number system: attributes of algebra, ordering, completeness, supremum and infimum with applications thereof; Sequences: definition, limit of sequences, limit theorems, monotone sequences, subsequences, Bolzano-Weierstrass sequence, Cauchy criteria, divergent sequences. Introduction to series; Function limit: definition, geometrical meaning, limit theorem, extended

• R. G. Bartle & D. R. Sherbert, Introduction to Real Analysis, 4rd ed., 2011, John Wiley & Sons, Inc.

• R.P. Burn, Numbers and Functions Steps into Analysis, 2nd ed., 2004,


concept of limit; Continuous function: Continuity and non continuity of function at a point and at a set, combination of continuous functions.

Cambridge University Press.

SCMA602151

ORDINARY DIFFERENTIAL

EQUATION (4 SKS)


Students are expected to be able to solve differential equations

First-order basic differential equations; Picard’s method, high-order ODEs; methods of solving high-order ODEs; Green’s function; Dynamic systems; using Frobenius’ sequence to solve DEs; Laplace transformation; Bessel functions; Legendre polynomials; Chaos

• W.E. Boyce & R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th ed, 2010, Wiley.

• E. Kreyszig, "Advanced Engineering Mathematics", 2000, John-Wiley & Sons.

• R.K. Nagle & E.B. Saff, & A.D. Snider, Fundamentals of Differential Equations and Boundary Value Problems, 6th ed., 2004, Addison-Wesley.

• C.H. Edwards & D.E. Penney, Elementary Differential Equations with Boundary Value Problems, 6th ed., 2008, Prentice Hall.

SCMA602161 DISCRETE

MATHEMATICS (3 SKS)


Students are expected to be able to explain discrete structures

Prime numbers, composite numbers, largest common factors, lowest common multiple, modular arithmetic, modulo m congruence, Euclidean algorithms, linear congruence, Chinese remainder theorem, Fermat’s little theorem; combinatorial analysis; discrete probability; inclusion-exclusion principle; pigeonholing; generating functions; recursive relations, z-transformations, relations, lattices, divide-and-conquer relations; code theory, Boolean algebra, graph theory, Eulerian and Hamiltonian graphs, planar graphs, trees, graph coloring and applications.


• Kolman/Busby/Ross, Discrete Mathematical Structures, 5th ed., 2003, Prentice Hall.

SCMA602211 MATHEMATICS SCMA601200 Explaining basic Probability and Distribution: Introduction: • Hogg, R.V. & Craig, A.T.


STATISTICS 1 (4 SKS)

(STATISTICS METHOD)

statistical concepts

Probability set functions, random discrete variables, continuous random variables, distribution functions and their attributes, Specific expectations; Multivariate distribution: Distribution of two random variables, Conditional probability, Conditional probability and expectations, correlation coefficient, independence of random variables, generalization of random variables; Special distributions: Binomial distribution, multinomial distribution, negative binomials, geometric and hypergeometric distributions, Poisson distribution, gamma and chi-square distribution, normal distribution, normal bivariate distribution, normal multivariate distribution; Distribution of random variable functions: Sampling theory, random discrete variable transformation, random continuous variable transformation, beta, t and F distribution, generalization of variable transformation techniques, moment-generating functions, distribution of X and "#$/&$, expectation of random variable function.

(1995), Introduction to Mathematical Statistics , Fifth Edition, Prentice-Hall, Inc.

• Hogg, R.V., McKean, J.W. & Craig, A.T. (2005), Introduction to Mathematical Statistics , Sixth Edition, Prentice-Hall, Inc.

• Ross, S. (2005). Mathematical Statistics with Applications, 6th Ed. Prentice-Hall, Inc. New Jersey.

• Hasset, M.J.& D.G. Stewart (1999). Probability for Risk Management. ACTEX Publications, Inc. Connecticut.

• Parzen, R.J. & M.L. Marx,

(2001), An Introduction to Mathematical Statistics and its Application, 3rd ed., Prentice Hall.

• Freund J. E. (1992), Mathematical Statistics, 5th Ed. Prentice-Hall, Inc. New Jersey. Ross, S. (2002), A First Course in Probability, Sixth Edition, Prentice Hall, Inc.

SCMA602212 MATHEMATICS

STATISTICS 2 (4 SKS)

SCMA602211 (MATHEMATICS STATISTICS 1)

Explaining basic statistical concepts

Limits of distribution: Ordered statistics, Chebyshev’s inequality; convergence in distribution and probability; limit of moment-generating functions; theorems of central limit and other theorems related to limits of distribution;

• Hogg, R.V. & Craig, A.T. (1995), Introduction to Mathematical Statistics , Fifth Edition, Prentice-Hall, Inc.


Estimated point for a single parameter: maximum likelihood and moment methods, unbiasedness, Consistency; concept of unbiased estimate with minimum variance for a single parameter. Complete single-parameter statistics: attributes of complete statistics. Completeness and uniqueness: exponential class of pdf, unbiased estimates with minimum variance for a function from a parameter. Rao-Cramer lower limit and Fisher information. Estimated interval of a parameter; introduction to testing of statistical hypotheses. Best tests: uniformly most powerful test, likelihood ratio test.

• Hogg R.V., Joseph W.M. & A.T. Craig (2005), Introduction to Mathematical Statistics, 6th Ed., Pearson Prentice Hall, New Jersey.

• Ross, S. (2005). Mathematical Statistics with Applications, 6th Ed. Prentice-Hall, Inc. New Jersey.

• Hasset, M.J.& D.G. Stewart (1999). Probability for Risk Management. ACTEX Publications, Inc. Connecticut.

• Freund J. E. (1992),

Mathematical Statistics, 5th Ed. Prentice-Hall, Inc. New Jersey. Larsen, R.J. & Morris L.M. (2001). An Introduction to Mathematical Statistics and Its Applications. 3rd Ed. Prentice-Hall, Inc. New jersey.

• Dudewicz,E.J & S.N. Mishra (1988). Modern Mathematical Statistics, John Wiley & Sons, New York.

SCMA602311 MATHEMATICS PROGRAMMING

(4 SKS)

SCMA601123 (LINEAR ALGEBRA); SCMA601111 (BASIC MATHEMATICS 2)

Explaining basic concepts of optimization problems

Covex functions; Kharus-Kuhn-Tucker optimal condition; optimization with limitations and solutions, linear programming, integer programming, quadratic programming, numeric approach of optimization problems without limitations, linear and multidimensional searches, Newton’s method and Aarh conjugate, penalty and

• M.S.Bazaraa,H.D.Sherali,andC.M.Shetty,Nonlinear Programming Theory and Algorithms, 2nd ed., 1990, John Wiley & Sons.

• S. G. Nash and A. Sofer, Linear and Nonlinear


barrier methods. Programming, 1996, McGraw-Hill. Nesa Wu & Richard Coppins, Linear programming and Extention, 1981, McGraw-Hill.

• W. L. Winston, Introduction to Mathematical Programming: Application & Algorithm, 2nd ed., 1995, International Thomson Publishing.

• S. G. Nash & A. Sofer, Linear and Nonlinear Programming, 1996, McGrow-Hill.

SCMA602402 NUMERICAL

METHODS (4 SKS)

SCMA601400 (ALGORITHM AND PROGRAMMING); SCMA601111 (BASIC MATHEMATICS 1); SCMA601123 (LINEAR ALGEBRA)

Students are expected to be able to explain basic concepts in algorithms and programming (C2)

Review of linear algebra, calculus, and algorithms; Vectors and vector norms, matrix and matrix norms, fixed-point convergence and theorems, round-off errors, efficiency, accuracy and stability, solutions for single-variable equations, approximation and interpolation; differentials and numeric integrals; direct and iterative methods for solving systems of linear equations.

• R. L. Burden dan J. D.Faires, Numerical Analysis, 9th edition, 2011, Brooks and Cole. Atkinson, Elementary Numerical Analysis, 2nd edition, 1985, John Wiley & sons.

• G.H. Golub and C.F.V Loan, Matrix Computations, 3rd ed, 1995, John Hopkins.

SCMA603533 FINANCE

MATHEMATICS (4 SKS)


1. Students are expected to analyze real-world problems and develop a corresponding mathematical model

2. /Students are expected to be able to complete mathematical models and analyze the data

Discussion of mathematical theory of simple interest, compound interest, present value, accumulated value, effective rate of interest and discount, force of interest and discount, varying interest, immediate annuity, due annuity, perpetuities, general annuities: rarely paid, with d.p. interest conv. Period, continuous annuity, yield rate, amortization, sinking fund, introduction to obligation.

• S.G. Kellison, The Theory of Interest,2nd ed., 1991, Irwin/McGraw-Hill Co., Boston.

• R. Cissel, Mathematics of Finance, 3rd ed., 1969, Houghton Mifflin Co.,Boston.

• F. Ayres, Mathematics of Finance, Schaum’ s, 1963, Mc Graw Hill.


obtained from them • M.M. Parmenter, Theory of Interest and Life Contingencies, with Pension Applications. 1999. Acted Publications: Winsted.

SCMA603132 ANALYSIS 2 (4 SKS)

SCMA602131 (ANALYSIS 1)

Students are expected to be able to explain basic concepts of real number analysis

Uniform continuity, Gauges, monotone functions and their inverses. Derivatives: definition and attributes, theorem of averages, L’Hopital’s rule, Taylor’s theorem, Riemann’s integral: Definition and attributes, functions using Riemann’s integral, basic theorems, approximation; function sequences: point of convergence and uniformity, limit exchange.

• R. G. Bartle & D. R. Sherbert, Introduction to Real Analysis, 4rd ed., 2011, John Wiley & Sons, Inc.

• M. C. Reed, Fundamental Ideas of Analysis, 1998, John Wiley & Sons, Inc.

SCMA603133 COMPLEX FUNCTION

(4 SKS)

SCMA602113 (BASIC MATHEMATICS 3); SCMA603114 (VECTOR CALCULUS)

Students are expected to be able to explain concepts in real numbers and complex functions

Complex numbers, analytic functions, elementary functions, mapping elementary functions, integrals, sequences, residual and pole, applications of residuals.

• J. W. Brown & R. V. Churchill, Complex Variables and Applications, 8thed., 2009, McGraw-Hill, Inc., International Editions.

• L.I. Volkovyskii, G.L. Lunts, and I.G. Aramanovich, translated by J.Berry, Translation edited by T. Kovari, A Collection of Problems on Complex Analysis, 1991, Dover Publications, Inc.

SCMA603134 TOPOLOGY (3 SKS)


Students are expected to use basic concepts in analysis and algebra in mathematical applications

Introduction; metric space; topological space; continuity and homomorphism; space made out of other spaces; connectedness; compactness; axiom of separation and countability; special topics of topology (contractive mapping on metric space, linear space with norms).

• J. R. Munkres, Topology, 2nd ed, 2000, Prentice Hall Inc, London.

• C. W. Patty, Foundations of Topology, 1993, International Thomson Publishing

SCMA603140 ANALYTIC GEOMETRY

SCMA601123 (LINEAR

Students are expected to use coordinate systems

Coordinate system, geometric objects in 2D (Lines, circles, ellipses) and their intersection, 3D

• Suryadi H.S, Geometri Analitik


(3 SKS) ALGEBRA) in geometry. (lines, circles, ellipses, spheres, ellipsoids, cones, conic sections) and their cross-sections

SCMA603152 MATHEMATICAL MODELLING

(4 SKS)

SCMA602211 (MATHEMATICS STATISTICS 1); SCMA602151 (ORDINARY DIFFERENTIAL EQUATION)

Students are expected to analyze mathematical models using basic mathematical concepts.

Understanding models and modeling; Mathematical models and types thereof; Models based on rate of change; Static and dynamic models; Deterministic and stochastic models; optimization models; mathematical models in various scientific disciplines.

• D.N. Burghus & M.M Borrie, Modeling with Differential Equation, 1982, Ellis Horwood Ltd. Walter J Meyer, Concepts of Mathematical Modeling, 1994, McGraw-Hill, Inc.

SCMA603153

PARTIAL DIFFERENTIAL EQUATION AND

BOUNDARY CONDITION

(3 SKS)

SCMA602151 (ORDINARY DIFFERENTIAL EQUATION)

Students are expected to be able to solve differential equations (C4)

Introduction (understanding and creating PDEs); first-order PDEs (linear and nonlinear); high-order PDEs (linear homogeneous constant-coefficient and linear non-homogeneous constant-coefficient PDEs); second-order variable-coefficient PDEs (specific types of second-order PDEs, variable separation, D’Alembert, 3D Laplace transformation, Fourier series); Applications of parabolic, hyperbolic and elliptic PDEs with exact and numeric solutions (finite difference method).

• Mayer, H & William B. Miller, Boundary Value Problems and Partial Differential Equations, 1992, PWS Kent, Boston.

• D. W. Trims, Applied Partial Differential Equations, 1990, PWS Publ.Co, Boston. Schaum series, Differential Equations,1975, Mc Graw Hill.

• R.L. Burden dan J. D. Faires, Numerical Analysis, 7th edition, 2001, Brooks and Cole;

SCMA603162 GRAPH THEORY (3 SKS)

SCMA602401 (DISCRETE MATHEMATICS)

Students are expected to be able to explain basic concepts of algebra and analysis in mathematical applications

Types of graphs; connectedness; Eulerian and Hamiltonian graphs; trees; graph coloring; planar graphs: Euler’s formula; dual graphs and chromatic polynomials.

• D.B. West, Introduction to Graph Theory, 2ed, 2001, Prenctice Hall.

• R. J. Wilson, Introduction to Graph Theory, 4thed, 1996, Longman Group.

SCST603010 REGRESSION ANALYSIS 1

(3 SKS)

SCMA602212 (MATHEMATICS STATISTICS 2); SCMA601123 (LINEAR

Students are expected to be able to analyze real-world problems and develop statistical models while providing

Introduction to simple linear regressions, assumptions in modeling, simple linear regression analysis, double linear regression analysis (matrix-based presentation, variance matrices, correlation, multicollinearity).

• Montgomery, et al, Introduction to Linear Regression Analysis, 3rded., 2001, John Wiley and Sons Inc.


ALGEBRA) contingencies if the assumptions of modeling are not met

Mathematical modeling, independent variables, qualitative and quantitative variables and interactions, noise and influential data, related ANOVA tables.

• W. Mendenhall, & T. Sincich, A Second Course in Statistics: Regression Analysis, 5th ed., 1996, Prentice Hall Inc, New Jersey.

• J. Neter, Kutner, MH, Nachtsheim, CJ, W. Wasserman, Applied Linear Statistical Models, 1996, Irwin Inc. (ISBN 0 – 256 – 11736 – 5).

• D.W. Hosmer, & S. Lemeshouw, Applied Logistic Regression, 2nd ed., 2000, John Wiley.

• A. Agresti, Categorical Data Analysis, 2nd ed., 2000, John Wiley.

SCMA603332 OPERATION RESEARCH

SCMA602212 (MATHEMATICS STATISTICS 2); SCMA602311 (MATHEMATICS PROGRAMMING)

Identifying characteristics of real-world optimization problems

Characteristics and principles of optimality deterministic dynamic and stochastic programming, real-world applications of dynamic programming, characteristics of queueing system, models of queueing, birth-death systems, Markov systems, real-world applications of queuing theory, using software to complete dynamic programs and queuing systems.

• L. Kleinrock & R. Gail, Queueing Systems-Problem and Solution, Volume I, 1996, John Wiley & Sons, New York.

• Gross, D & Harris, CM. (1985), Fundamentals of Queueing Theory 2nd ed. John Wiley & sons,USA

• Cooper, L. & Cooper, M. W. Introduction to Dynamic Programming. Pergamon Press, 1981.

• Hillier, F.k S. & Lieberman, G. J. Introduction to Operations Research. McGraw- Hill, 1995.

• Parlar,M..InteractiveOperatio


nsResearchwithMAPLE:MethodsandModels. Birkhauser, 2000.

• Ravindran, A., Phillips, Don T., &Solberg, J. J.Operation Research:Principlesand Practice. John Wiley & Sons, Inc, 1987.

• Sniedovich, M.. Dynamic Programming. Pure and Applied Mathematics Series, Marcel Dekker, Inc, 1992.

• Taha, H. A. Operations Research: An Introduction. Prentice-Hall, 1997.

• Winston, W. L. Introduction to Mathematical Programming: Applications and Algorithms. Duxbury Press, 1995.

SCMA603331 NETWORK

OPTIMIZATION ( 3 SKS )

SCMA602401 (DISCRETE MATHEMATICS); SCMA602311 (MATHEMATICS PROGRAMMING)

Students are expected to be able to choose the methods for solving optimization problems

Basic definitions, design, analysis and theory of networks; shortest-path algorithms; algorithms for minimum spanning trees, planar graphs, maximum flow and cost flow; generalization of flows problems; multicommodity flows, case studies.

• R. K Ahuja, T. L Magnanti, J. B Orlin, Network Flows,1993, Prentice Hall Inc, New Jersey.

• J.R. Evans, E. Minieka, Optimization Algorithms for Network and Graphs,2nded., 1992, Marcel Dekker.


SCMA603341

CONTROL OPTIMAL THEORY

(3 SKS)

SCMA602151 (ORDINARY DIFFERENTIAL EQUATION); SCMA602311 (MATHEMATICS PROGRAMMING)

Students are expected to be able to choose the methods for solving optimization problems

Calculus variation problems: Euler’s equation; transversality condition, autonomous systems, diagram analysis. Optimal control theory: types of endpoint applications in investment and advertisement, Pontryagin’s principle, dynamic programming, optimal stochastic control.

• M.I. Kamien & N. L. Schwartz, Dynamic Optimization, North-Holland, (TokuBeeng). Bertsekas, Dynamic Programming, 2000, Prentice Hall.

SCMA603421 PARALLEL

COMPUTATION (3 SKS)

SCMA601400 (ALGORITHM AND PROGRAMMING)

Students are expected to be able to diagnose real-world problems in parallel programming.

Parallel computation architecture, programming concepts based on similar memory, shared and hybrid memory, related implementations of parallel programming (examples of OpenMP, MPI, CUDA, accelerated programming).

• Akl SG, The Design and Analysis of Parallel Algorithms, 1989, Prentice-Hall.

• P. S. Pacheco & W. C. Ming, Introduction to Message Passing Programing : MPI User Guide in Fortran, 1997, Technical Rep., University of Hongkong.

• J. Radajewski & D. E., Beowulf How To, 1998, GNU General Public Lic.

SCMA603431 NUMERICAL

MATHEMATICS (3 SKS)

SCMA602402 (NUMERICAL METHODS)

Students are expected to be able to solve mathematical problems with numeric approximation.

Approximation theory: least squares, orthogonal polynomial, Chebyshev, trigonometry, fast Fourier transformation, approximation of eigenvalues and matrix factorization: power method, householders, QR, singular value decomposition; numeric solutions of nonlinear methods: Newton’s method, Quasi-Newton’s method, steepest descent.

• R.L. Burden dan J.D. Faires, Numerical Analysis, 9th edition, 2011, Brooks and Cole.

• G.H. Golub and C.F.V Loan, Matrix Computations, 3rd ed, 1995, John Hopkins.

• C.T., Kelley, Iterative Methods for Linear and Nonlinear Equations, 1995, SIAM.

SCMA603432 SCIENTIFIC

COMPUTATION (3 SKS)

SCMA602402 (NUMERICAL METHODS); SCMA602151 (ORDINARY

Solving applications of various problems such as upper and lower bounds, and stochastic differential equations

Solutions to odinary differential equations (ODEs); initial value problems and limit value problems will be solved using numeric methods. Discussion of stochastic differential equations including Brownian motion, stochastic integrals, Ito’s

• P. E. Kloeden & Eckhard Platen, Numerical Solution of Stochastic Differential Equations, 1995, Springer.

• P. E. Kloeden,Eckhard


DIFFERENTIAL EQUATION); SCMA602211 (MATHEMATICS STATISTICS 1)

(C4) formula, numeric methods which can be used, analysis of convergence and stability of numeric methods for ODEs and models of ODEs for certain applications. Discussion of these topics is accompanied by computer simulations during tutorials.

Platen & H. Schurz, Numerical Solution of SDE Through Computer Experiments, 1993, Springer.

• S. Cyganowski, P. Kloeden & J. Ombach, From Elementary Probability to SDEs with Maple, 2002, Springer.

• M. T Heath, Scientific Computing : An introductory Survey, 1999, McGraw Hill.

SCMA603441

DESIGN AND ANALYSIS

ALGORITHM (3 SKS)

SCMA601400 (ALGORITHM AND PROGRAMMING); SCMA602403 (STRUCTURAL COMPUTATION); SCMA602401 (DISCRETE MATHEMATICS)

Students are expected to be able to analyze the complexities of algorithms in mathematical problems

Efficiency and measurement of running time, asymptotic notation, best-case and worst-case algorithm efficiency analysis and recursive analysis of algorithms, brute-force, divide-and-conquer, greedy, and dynamic programming algorithms, algorithms on graphs, probabilistic algorithms, introduction to parallel algorithms.

• K. A. Berman, Jerome L. Paul, Fundamentals of Sequential and Parallel Algorithms, 1997, ITP.

• G. Brassard, P. Bratley, Algorithmics, Theory & Practice, 1988, Prentice-Hall.

• C. Thomas H, Leiserson Charles E., Rivest Ronald L., Introduction to Algorithms, 1991, McGraw Hill.

• G. L.Heileman, Data Structures, Algorithm and Object Oriented Programming, 1996, McGraw Hill.

SCMA603901 RESEARCH

METHOD (2 SKS)

Minimum credit earn 114 credits

Students are expected to be able to explain the basics and steps of research and scientific writing.

Research as a means of obtaining facts; types and methods of research; determining research topics; concepts of variables and systems of variables; development of hypotheses; research plans and steps; relations and nuisance variables; methods of experimentation; sources of errors and generalizations; survey methods and constructing questions in surveys; sampling methods; validity

• M. Walizer, & P. L. Wunier., Research Methods and Analysis, 1978, Harper & Row. David Lindsay, (alih bahasa: Suminar Setiadi Achmadi), Penuntun Penulisan Ilmiah (judul asli: A Guide to Scientific


and reliability; tutorials in making reseach proposals; writing research reports.

Writing), 1988, UI Press, Jakarta.

• D. V. Seyler, Doing Research: The Complete Research Guide, 2nd edition, 1999, Mc Graw Hill College.

• W. C. Booth, Gregory G. Colomb, & Joseph M. Williams, The Craft of Research, 1995, The University of Chicago Press.

SCMA604123 LINEAR

ALGEBRA 2 (3 SKS)

SCMA602122 (ALGEBRA)

Students are expected to be able to explain the concept of basic algebraic structures

Vector space, linear transformation, Eigenvalues, norms and results, isometry. Spectral theorems, singular value decomposition, Cayley-Hamilton theorem, Jordan form, direct-sum decomposition.

• A. Arifin, Aljabar Linier, edisi II, 2001, Penerbit ITB.

• P.l R. Halmos, Finite Dimensional Vector Spaces, 1987, Springer-Verlag. Bill Jacob, Linear algebra, 1990, W.H. Freeman and Company.

SCMA604135 FUNCTIONAL

ANALYSIS (3 SKS)

SCMA602131 (ANALYSIS 1); SCMA602122 (ALGEBRA)

Students are expected to be able use basic concepts of analysis and algebra in mathematical applications

Metric space, Banach space, linear operators, Hilbert space, adjoint space, Hahn-Banach theorem, Riesz representation.

• E. Kreyszig, Introductory Functional Analysis With Applications, 1978, John Wiley & Sons

• J. Tinsley Oden, Leszek F. Demkowicz, Applied Functional Analysis, 1996, CRC Press Eberhard Zeidler, Applied Functional Analysis (Applications to Mathematical Physics), Applied Mathematical Sciences 108, 1995, Springer Verlag

SCMA604136 MEASURE THEORY

(3 SKS)


Students are expected to be able use basic concepts of analysis and

Measured functions; measurements; integrals; integrated functions; Lebesque space (Lp), mode of convergence; measuring decomposition,

• R. G. Bartle, The Elements of Integration & Lebesgue Measure, 1966, John Wiley


algebra in mathematical applications

generation of measures, applications of measure theory and integration in other areas of study.

& Sons, Inc., Canada. • M. Capinski & E. Kopp,

Measure, Integral and Probability, 2nd ed., 2004, Springer-Verlag.

• M. Adams and V. Guillemin, Measure Theory and Probability, 1996, Birkhauser, Boston.

SCMA604412 COMPUTATION

THEORY (3 SKS)

SCMA601400 (ALGORITHM AND PROGRAMMING); SCMA602401 (DISCRETE MATHEMATICS)

Students are expected to be able to explain abstract mathematical machines and formal language which forms the basis of computer science theory.

Discrete machines and automata; Turing machines; languages and semantics; connection between abstract machines and semantics; computability.

• J. C. Martin, Introduction to Languages and the Theory of Computation, 4th Ed., Mc Graw Hill, 2011.

• H. R. Lewis, C.H. Papadimitrou, Elements of the Theory of Computation, Prentice hall, 1981.

• M. Sipser, Introduction of the Theory of Computation, 2nd Ed., Thompson Course Technology, 2006.

SCMA604541 SURVIVAL ANALYSIS

(3 SKS)


Students are introduced to statistical analysis techniques for time-to-event data, and are expected to correctly explain time-to-event data for analysis and modeling, as well as use various statistical analysis techniques on censored or truncated survival time data

Basic quantities of survival functions: Introduction – examples and data types of survival analysis; survival, hazard, mean residual life and median life functions, parametric models for survival data, truncation and censoring; Introduction, left and right censoring or intervals, truncation, constructing likelihood for truncated or censored data, non-parametric estimates on right-censored and left-truncated data: Introduction, estimation for survival functions and cumulative hazard for right-censored data, pointwise confidence interval for survival functions, confidence band for survival functions, point and interval estimation for mean and median survival times, estimators for survival functions for truncated and censored data, testing

• J. P. Klein, & M. L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, 1997, New York: Springer-Verlag Inc.

• D. London, Survival Models and their simulation, 1998, Actex Publications.

• M. Gauger, Course 3 Student Manual (Vol.1), 2000, Actex Publications.

• J. D. Kalbfleisch &R. L. Prentice, The Statistical Analysis of Failure Time


hypotheses: Introduction, single-sample tests, multi-sample tests, trend tests, semiparametric proportional hazard regression with constant covariant: Introduction, partial likelihood for data times to distinct events, partial likelihood in the event of ties, local and global testing.

Data, 1980, John Willey & Sons, New York.

SCST603103 TIME SERIES

ANALYSIS (3 SKS)


Students are expected to be able to explain various statistical forecasting methods in business applications, such as exponential smoothing, seasonal decomposition, etc. There is an incentive to use this method on real data using a full set of features such as those found in spreadsheet programs, such as Excel.

Autocorrelation and its functions; partial autocorrelation and its functions; trends and seasonal influences, estimations and forecasting; mathematical modeling; autoregressive moving average process and ARIMA.

S. C. Wheelwright dkk, Forecasting: Methods and Applications, 3rd edition 2008, Wiley.

S. A. Delurgio, R. D Irwin, Forecasting Principles and Applications, 1st edition 1998.

SCMA603114 VECTOR

CALCULUS (2 SKS)


Students are expected to be able to explain basic concepts in calculus

Vectors, functions with vector values and curvilinear motion, vector fields, vector differentiation, gradients, divergence, curl, line integrals, divergence theorem, Stokes’ theorem and Green’s Theorem.

• D. Varberg and E.S Purcell, Calculus, 9th ed, 2007, Prentice-Hall.

• M. R., Spiegel., Vector Analysis, 2nd ed., Schaum’s Series, 1981, McGraw Hill

SCMA603403 STRUCTURAL

COMPUTATION (3 SKS)

SCMA601400 (ALGORITHM AND PROGRAMMING)

1. Students will know more about the basics of structured, modular and object-oriented programming.

2. Students are expected to be able

Concepts of structured programming, modular programming, procedures and functions, call-by-value and call-by-reference, recursive and iterative functions, object-oriented programming, data abstraction concepts, data structures (static and dynamic), classes, arrays, pointers, linked lists, stacks and queues, trees and graphs, using efficient algorithms in applications which utilize

• G. L.Heileman, Data Structures, Algorithm and Object Oriented Programming, 1996, McGraw Hill.

• Data Structures and Algorithm Analysis in C++ (3rd edition), by M. A. Weiss. Addison-Wesley


to design and use data structures which are appropriate and efficient for structured, modular and object-oriented programming to aid computer-assisted problem-solving.

programming and data structures such as: sorting and searching algorithms, tutorials on structured and object-oriented programming languages such as R and Python.

• T. Budd, An Introduction to Object Oriented Programming (3rd) editition, Pearson 2001


5. AUTHORITY OF CURRICULUM PURPOSE AND CURRICULUM REVIEW

The 2016 curriculum Mathematics Study Program was prepared by the Curriculum Team of

Mathematics Department of FMIPA UI consisting of Professors and teaching staff. The curriculum is

then taken to the Department's plenary session to obtain feedback on improvement and ultimately to

be approved by the Mathematics Department of FMIPA UI. As in other Studies Program at FMIPA

UI, the curriculum will be evaluated maximally after 5 years in order to maintain the quality of

education and scientific development.

The authority of institutional curriculum revision is the authority of FMIPA UI. This revision is

an obligation of the Study Program, so for perfection it needs input from all stakesholders from inside

and outside, benchmarking with universities or institutions at home and abroad (at least by studying

curriculum from overseas university online), bringing or discussing with domestic best partner, and

pay attention to the agreement or decision made by Indonesian Mathematical Society (IndoMS).


6. OPPORTUNITIES FOR STUDENTS TO DEVELOP THEMSELF

Bachelor of Mathematics is currently highly needed in various fields of work and the opportunity to

continue his studies to further levels. The opportunities are generally:

• Working in various domestic governmental and research institutions including: Ministry of

Finance, Trade, Industry, National Education, Home Affairs, Communications, Health,

Agriculture, Forestry, Fisheries and Marine, Mining and Energy, Transportation,

Environment, Defense, Law and Legislation, BPS, LIPI, BPPT, BATAN, Universities,

Population, Family Planning, BUMN, Meterology and Geofiska, BAPEDAL / SARPEDAL,

BKPM.

• Extensive job opportunities in finance and banking, among others: BI, State-Owned and

Private Banks, Financial Services (among others OJK), Stock Exchanges, Insurance /

Actuarial.

• Job opportunities in the business sector, among others: Marketing Research, Strategic business

planning, Industry, production, manufacturing, telecommunications, media, quality

management, inventory system.

• Other private employment opportunities, including survey institutions for the purposes of:

politics (pilkada, pilpres, pilgub, etc.), popularity of candidates, quick counts, etc.; Advertising

research, HRD researchers.

• Opportunities to continue studying S2 and S3, both at home and abroad.


7. INSTITUTION REFERENCE

The curriculum of the Undergraduate Mathematics Program refers to both undergraduate and

postgraduate programs at renowned universities, institutions and professional organizations engaged in

or related to mathematics, both from within and outside the country.

a. Universities, institutions, domestic mathematical organizations, among others:

i. Department of Mathematics FMIPA ITB Bandung.

ii. Department of Mathematics, FMIPA Institute of Technology Surabaya (ITS),

Surabaya

iii. Mathematics Study Program, FMIPA Universitas Gadjahmada (UGM), Yogyakarta

iv. The Indonesian Mathematical Society (IndoMS),

b. Universities, institutions, foreign mathematical organizations, among other

i. American Mathematical Society (AMS), USA.

ii. MIT, USA

iii. University of Harvard, USA

iv. University of Arizona, USA


8. REFERENCE

Mendiknas. (2000). SK Mendiknas No 232/U/2000. Pedoman Penyusunan Kurikulum Inti Pendidikan

Tinggi Dan Penilaian Hasil Belajar Mahasiswa. Jakarta.

Mendiknas. (2002). SK Mendiknas No. 45/U/2002. Kurikulum Inti Pendidikan Tinggi. Menteri

Pendidikan Nasional. Jakarta.

Majelis Wali Amanat Universitas Indonesia. (2005). Peraturan MWA UI Nomor

006/Peraturan/MWA-UI/2005. Evaluasi Hasil Belajar Mahasiswa Pada Program Pendidikan di

Universitas Indonesia. MWA UI. Jakarta

Direktorat Pengembangan Akademik, 2012. Pedoman Penyusunan Kurikulum Berbasis Kompetensi

(KBK) Universitas Indonesia. Edisi ke-2. Jakarta

Presiden (2012). Peraturan Presiden No. 8 Tahun 2012. Kerangka Kualifikasi Nasional Indonesia

(KKNI). Jakarta.


Documents

Kurikulum Prodi S1 Matematika UI rev 1 April English Dipo · 2018-04-04 · Curriculum Document, Undergraduate Study Program Mathematics, Faculty of Mathematic and Natural Sciences,