Mohd Khairulzamani Bin Mohammad PISMP Matematik 1

Course Pro Forma Program Ijazah Sarjana Muda Perguruan Dengan Kepujian

(Matematik Pendidikan Rendah)

Course Title Applications of Mathematics (Aplikasi Matematik)

Course Code MTE3114

Credit 3(2+1)

Contact Hours

60 hours

Language Of Delivery

English Language

Prerequisite to entry

Nil

Semester One/ Two

Learning outcomes

1. Explore the role of mathematics in modern technologies.

2. Investigate mathematics as an ongoing cultural activity

3. Demonstrate an understanding of the nature of mathematics

and its applications

4. Apply the various mathematical processes and problem solving techniques in real life

Synopsis This course focuses on the applications of mathematics in various areas. Its contents cover mathematics in everyday life, classical codes and ciphers, codes and cryptography, use of mathematical modeling in biology and ecology, and some key mathematical ideas related to calculus. Experience involving applications of mathematics is provided through practical activities.

Kursus ini berfokus kepada aplikasi matematik dalam pelbagai bidang. Isi kandungannya meliputi matematik dalam kehidupan harian, kod klasik dan nombor rahsia, kod dan kriptografi, penggunaan model matematik dalam biologi dan ekologi, serta sebahagian idea utama matematik berkaitan dengan kalkulus. Pengalaman melibatkan aplikasi matematik dibekalkan melalui aktiviti-aktiviti praktikal.

Mohd Khairulzamani Bin Mohammad PISMP Matematik 1

Topic Content Hours

1

Theory Mathematics in everyday life

Role of mathematics in modern technologies

Mathematics as an ongoing cultural activity

Bases for contemporary mathematics

4

2 Classical codes and ciphers

The development of classical codes and ciphers using the following techniques o Transposition o Substitution

4

3 Codes and cryptography

Error correcting codes: repetition codes, parity check codes, Hamming codes, Hadamard codes and the 1969 Mariner spacecraft

Linear codes: solution spaces for systems of linear equations and their use in error correcting codes

Public-key cryptography, including the use of elementary number theory to produce computationally intractable systems of codes, the RSA algorithm

6

4 Use of mathematical modeling in biology and ecology

Predator-prey models: separate and non-separate generations, the logistic equation, interactions between species, simulations

The use of simple differential equations in modeling safe and effective drug dosages

Modeling the spread of diseases such as AIDS, bird flu etc

10

5 Some key mathematical ideas related to calculus

Archimedes’ approximation of π

Archimedes’ determination of the area of a circle

Zeno’s paradox

Newton’s investigation of cubic curves

6

Sub Total 30

Mohd Khairulzamani Bin Mohammad PISMP Matematik 1

1

Practical Mathematics in everyday life

Investigate the following o Role of mathematics in modern

technologies o Mathematics as an ongoing cultural

activity o Bases for contemporary mathematics

Compile the findings

Submit a written report

10

2 Mathematical modeling

Conduct a mathematical modeling activity based on the following steps o Specify a real problem o Formulate a mathematical model o Solve the mathematical problem o Interpret the solution o Compare with reality o Communicate the results

Group presentation

Submit a written report

10

3 Some key mathematical ideas related to calculus

Group project o Explore applications and relations of the

following Archimedes’ approximation of π Archimedes’ determination of the area

of a circle Zeno’s paradox Newton’s investigation of cubic curves

o Presentation of project

10

Sub Total 30

Total 60

Assessment Coursework 60% Examination 40 %

Main References

Coutinho, S. C. (1999). The mathematics of ciphers: Number theory and RSA Cryptography. Natick, MA: A. K. Peters.

Dym, C. L. (2004). Principles of mathematical modelling. 2nd ed.

Boston: Elsevier Academic Press. Haydock, R. (1991). Information and coding. UK: Cambridge.

Mohd Khairulzamani Bin Mohammad PISMP Matematik 1

Stacey, K. & Stillman, G. (2002). Modelling trends in numbers of

deaths due to HIV/AIDS infection in USA and Australia. Melbourne:

University of Melbourne, CAS-CAT Project. Wilf, H. S. (1986). Algorithms and complexity. Englewood Cliffs, NJ:

Prentice-Hall.