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Mathematics Major Proposal, page 1

Department of Mathematics

Proposal

Revised Major and Change of Numbering System

Synopsis

The Department of Mathematics proposes effective Fall Semester, 2003 the following courses be required for completion of a Bachelor of Science degree: Track I:Core Major Courses (33 hours): Calculus I, Calculus II, Calculus III, Set Theory, Linear Algebra, Real Analysis I, Real Analysis II, Abstract Algebra I, Abstract Algebra II, and Senior Seminar. Additional Mathematics Courses (9 hours): The student must take either Ordinary Differential Equations or Probability and Statistics I. The student must also take two other mathematics courses at the 300 level or above at least one of which is at the 400 level. Cognate Courses (18 hours): The student must take one three hour course in computer programming. The student is required to complete one course sequence (two courses) from the approved cognate course list (see page 4). The student is required to complete three other courses from the approved cognate course list for the B. S. (see page 4). Track II:Core Major Courses (33 hours): Calculus I, Calculus II, Calculus III, Set Theory, Linear Algebra, Ordinary Differential Equations, Probability & Statistics I, Real Analysis I, Abstract Algebra I, and Senior Seminar. Additional Mathematics Courses (9 hours): The student must take either Real Analysis II or Abstract Algebra II. The student must also take two other mathematics courses at the 300 level or above. Cognate Courses (18 hours): The student must take one three hour course in computer programming. The student is required to complete one course sequence (two courses) from the approved cognate course list (see page 4). The student is required to complete three other courses from the approved cognate course list for the B. S. (see page 4).

Thus, the total course load required for the B. S. in mathematics is 60 hours.Presently, the total course load required for the B. S. in mathematics is 60 hours. The sixty hours are divided as

follows. The courses required for the B. S. are Principles of Mathematics, Calculus I, Calculus II, Calculus III, Set Theory, Linear Algebra, Real Analysis I, Abstract Algebra I, Abstract Algebra II, Senior Seminar, and one additional course at the 400 level (35 hours); while an additional 25 hours of other approved cognate electives in science or mathematics is to be completed in order to earn the degree.

The Department of Mathematics proposes effective Fall Semester, 2003 the following courses be required for completion of a Bachelor of Arts degree: Core Major Courses (27 hours): Calculus I, Calculus II, Calculus III, Set Theory, Linear Algebra, Real Analysis I, Abstract Algebra I, and Senior Seminar. Additional Mathematics Courses (15 hours): The student must take either Real Analysis II or Abstract Algebra II. The student must take either Ordinary Differential Equations or Probability and Statistics I. The student must also take three other mathematics course at the 300 level or above at least one of which is at the 400 level. Cognate Courses (18 hours): The student must take one three hour course in computer programming. The student is required to complete five other courses of the student’s choice that are approved by his advisor and the mathematics department chairman.

Thus, the total course load required for the B. A. in mathematics is 60 hours. Presently, the total course load required for the B. A. in mathematics is 60 hours. The sixty hours are divided as

follows. The courses required for the B. A. are Calculus I, Calculus II, Calculus III, Set Theory, Linear Algebra, Real Analysis I, Abstract Algebra I, Abstract Algebra II, Senior Seminar, and one additional course at the 400 level (35 hours); while an additional 25 hours of other approved cognate electives is to be completed in order to earn the degree.

The Department of Mathematics proposes effective Fall Semester, 2003 that the Principles of Mathematics (Math 180 under the old numbering system; Math 157 under the new numbering system) be changed from a 2 credit course to a three credit course. Justification for this is both practical as well as pedagogical.


The Department of Mathematics proposes effective Fall Semester, 2003 a restructuring of the mathematics program course numbering system. Primary coding would be such that the first digit of a course would reflect the expected enrolment status of the average student taking the course. Courses intended primarily to be completed in the freshman year be at the 100 level; courses intended primarily to be completed in the sophomore year are at the 200 level; courses intended primarily to be completed in the junior year are at the 300 level; and, courses intended primarily to be completed in the senior year are at the 400 level. Secondary coding of course would begin at the 150 level or above such that the second digit of a course would reflect content area. A zero would be a basic course, a 1 would be a service course for other departments, a two would be an applied course, a three would be reserved for future use, a four would be a stochastic course, a five would be a foundations course, a six would be an analysis course, a seven would be an algebra course, an eight would be geometry or topology course, and a nine would be a special topics course. Ternary coding of courses begins at the 150 level or above such that the third digit of a course would reflect sequence of a course. A zero would reflect a core course, a one, two, and three would reflect a sequence of first, second, and third courses of a sequence. Any other digit would reflect the course is non-sequential.

Detailed Description

Coding x1 x2 x3 x1: 0 remedial x2: 0 basic x3: 0 basicbegins at 1 freshman 1 service for other majors 1 first of sequence 151 level 2 sophomore 2 applied 2 second of “

3 junior 3 < for future use> 3 third of “ 4 senior 4 probability and statistics 5, 7, or 9 other

5 foundations 8 directed reading6 analysis 4 < for future use>7 algebra 6 < for future use>8 topology or geometry9 special topics

Core Curriculum Courses:

Number Title Prerequisite HoursMath 090 Basic Mathematics (Math 051) 01

Math 100 College Algebra (Math 100) Math 090 (051) 3Math 110 Finite Math (Math 140) Math 100 (100) 3Math 120 Pre-calculus (Math 154) Math 100 (100) 3Math 130 Basic Statistics (Math 155) Math 110 3Math 157 Principles of Mathematics (Math 180) Math 120 3Math 160 Calculus for Business (Math 250) Math 110 or 120 3Math 161 Calculus I (Math 251) Math 120 4Math 162 Calculus II (Math 252) Math 161 4

CORE CURRICULUM SATISFIED BY: sequence Math 100 & 110 (Division of Humanities), Math 100 & 120 (Division of Business and Economics or Division of Science and Mathematics (non-mathematics major)), Math 161 & 162 (Department of Mathematics). Alternate satisfaction: sequence Math 110 & 130 (Division of Humanities); Math 120 & 160 (Division of Business and Economics); Math 130 & 160 (Division of Business and Economics); Math 120 & 157 (Division of Business and Economics or Division of Science and Mathematics (non-mathematics major)); Math 120 & 161 (Division of Business and Economics or Division of Science and Mathematics (non-mathematics major)); or, Math 161 & 162 (Division of Business and Economics or Division of Science and Mathematics). Any other sequence must be approved by the Department of Mathematics.

1 Institutional Credit only. The course meets 3 hours per week.


Course Numbering

New Number New Title (old title or number) Prerequisite HoursMath 090 Basic Mathematics (Math 051) 0Math 100 College Algebra (Math 100) Math 090 3Math 110 Finite Math (Math 140) Math 100 3Math 120 Pre-calculus (Math 154) Math 100 3Math 130 Basic Statistics (Math 155) Math 110 3Math 157 The Principles of Mathematics (Math 180) Math 120 3Math 160 Calculus for Business (Math 250) Math 110 or 120 3Math 161 Calculus I (Math 251) Math 120 4

(renamed from Analysis I)Math 162 Calculus II (Math 252) Math 161 4

(renamed from Analysis II)Math 211 Introduction to Discrete Mathematics (Math 280) Math 110 or 120 3Math 255 Introduction to Set Theory Math 161 3Math 263 Calculus III (Math 351) Math 162 4

(renamed from Analysis III)Math 271 Introduction to Linear Algebra (Math 272) Math 161 3Math 321 Introduction to Ordinary Differential Equations (Math 365) Math 162 3Math 325 Applied Mathematics I (Math 367) Math 263 and 321 3Math 327 Applied Mathematics II (Math 368) Math 325 3Math 341 Probability and Statistics I (Math 355) Math 255 or 211; and 162 3Math 342 Probability and Statistics II (Math 356) Math 341 and 263 3 Math 361 Real Analysis I (Math 353)

(renamed from Advanced Calculus) Math 255 and 263 3Math 362 Real Analysis II (Math 354)

(renamed from Advanced Calculus II) Math 361 and 271 3Math 371 Abstract Algebra I Math 255 or 211; and 271 3Math 372 Abstract Algebra II Math 371 3Math 391 Special Topics in ____ To Be Determined (T. B. D.)

depending on subject 1, 2, or 3Math 398 Directed Reading Math 255, T. B. D. 1, 2, or 3

depending on subjectMath 463 Real Variables (Math 451) Math 362 3Math 465 Complex Variables (Math 454) Math 361 3Math 467 Numerical Analysis (Math 457) Math 271 and 321 3Math 475 Number Theory (Math 461) Math 371 3Math 485 Topology (Math 480) Math 361 3Math 487 Differential Geometry (Math 482) Math 361 and 271 3Math 497 Senior Seminar (Math 495) Math 361 and 371. 3Math 498 Directed Reading and Research Math 361, 371, or 398 & 1, 2, or 3

T. B. D. depending on subject


Degree Requirements2: Bachelor of Science in Mathematics track I: Requires Math 161, 162, 255, 263, 271, (341 or 321), 361, 362, 371, 372, 497, and 2 other mathematics courses at the 400 level or 1 other 300 level and one other 400 level (42 hours). In addition the student must take one three hour course in computer programming. The student is required to complete one sequence (two courses) of other mathematics or science courses from the approved cognate course list (for example: Mathematics 341 & 342, Biology 111 & 112 or Computer Science 110 & 160) selected by the student in consultation with his advisor and that is approved by the department. The student is required to complete three other courses from the approved cognate course list for the B.S. The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. S. in mathematics is 60 hours.

Bachelor of Science in Mathematics track II: Requires Math 161, 162, 255, 263, 271, 321, 341, 361, 371, (362 or 372), 497, and 2 other mathematics courses at the 300 level or above (42 hours). In addition the student must take one three hour course in computer programming. The student is required to complete one sequence (two courses) of other mathematics or science courses from the approved cognate course list (for example: Mathematics 341 & 342, Biology 111 & 112 or Computer Science 110 & 160) selected by the student in consultation with his advisor and that is approved by the department. The student is required to complete three other courses from the approved cognate course list for the B.S. The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. S. in mathematics is 60 hours.

Bachelor of Arts in Mathematics: Requires Math 161, 162, 255, 263, 271, (321 or 341), 361, 371, (362 or 372), 497 and 3 other mathematics courses at the 300 or 400 level at least one of which is at the 400 level (42 hours). In addition, the student is required to complete 18 hours of cognate electives selected by the student in consultation with his advisor and approved by the chairman of the mathematics department. A three hour course in computer programming must be included in the eighteen hours of cognate electives. . The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. A. in mathematics is 60 hours.

Currently (at least 1979 to present): The math for either degree must include: Math 157 (180), 161 (251), 162 (252), 255, 271 (272), 263 (351), 361 (353), 371, 372, 497 (495), and one additional 400 level course.

Approved list of cognate electives for the B. S. include; but, are not limited to:

Mathematics 321Mathematics 325Mathematics 327Mathematics 341Mathematics 342Mathematics 391Mathematics 398Mathematics 463Mathematics 465Mathematics 467Mathematics 475

Mathematics 485Mathematics 487Mathematics 498Biology 111Biology 112Biology 220Biology 251Biology 300 or aboveChemistry 111Chemistry 112Chemistry 211

Chemistry 231Chemistry 232Chemistry 300 or aboveComputer Science 110Computer Science 160Computer Science 260Computer Science 285Computer Science 300 or aboveEngineering 201

Engineering 205Engineering 206Engineering 300 or aboveEconomics 201Economics 202Economics 300 or abovePhysics 154Physics 253Physics 254Physics 300 or above

Suggested pace:Freshman YearMath 161, 162 plus core curriculum coursesSophomore YearMath 255, 263, 271 plus finish core curriculum coursesJunior Year321 or 341, 361, 362, 371, 372 plus other science or mathematicsSenior Year497, 2 other 400 levels, or 1 other 300 level and one other 400 level plus other science or mathematics

2 Added requirements highlighted


NEW MAJOR REQUIRED HOURS OLD REQUIRED HOURS

minimum B. S. minimum B. S.42 hours mathematics / 18 math or science cognates/ 60 other 35 math / 25 math or science cognates/ 60 other.

maximum B. S.54 hours mathematics /6 other science cognates/ 60 other.

minimum B. A. minimum B. A. 42 hours mathematics / 18 cognates / 60 other 35 math / 25 math or science / 60 other .

maximum B. S.54 hours mathematics /6 other science cognates/ 60 other

Model Plan of Study for B. S. in Mathematics Track I

Freshman Year

First Semester Second SemesterMath 161 4 Math 162 4English 101 3 CSC 110 (Programming Cognate) 3History 111 3 English 102 3Music 111 3 History 112 3Edu 151 0 Psychology 101 3Edu 153 0 Edu 152 0HPED 151 1 Edu 154 0 total hours 14 total hours 16 30

Sophomore Year

First Semester Second SemesterMath 263 4 Math 271 3Math 255 3 Math or Science Cognate Elective 3MFL 201 3 MFL 202 3English 250 3 Religion 201 3Edu 251 0 Physics 154 4HPED 154 1 Edu 252 0 total hours 14 total hours 16 60

Junior Year

First Semester Second SemesterMath 361 3 Math 362 3Math 371 3 Math 372 3Math 321 or 341 3 Math or Science Cognate Elective 3Art 110 3 Math or Science Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (400 level) 3Math Elective (300 or 400 level) 3 Math or Science Cognate Sequence 3Math or Science Cognate Sequence 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3

total hours 16 total hours 14 120


Model Plan of Study for B. S. in Mathematics Track II

Freshman Year


Sophomore Year


Junior Year

First Semester Second SemesterMath 361 3 Math 341 3Math 371 3 Math 362 or 372 3Math 321 3 Math or Science Cognate Elective 3Art 110 3 Math or Science Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (300 or 400 level) 3Math Elective (300 or 400 level) 3 Math or Science Cognate Sequence 3Math or Science Cognate Sequence 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3



Model Plan of Study for B. A. in Mathematics

Freshman Year


Sophomore Year

First Semester Second SemesterMath 263 4 Math 271 3Math 255 3 Cognate Elective 3MFL 201 3 MFL 202 3English 250 3 Religion 201 3Edu 251 0 Physics 154 4HPED 154 1 Edu 252 0 total hours 14 total hours 16 60

Junior Year

First Semester Second SemesterMath 361 3 Math 362 or 372 3Math 371 3 Math Elective (300 or 400 level) 3Math 321 or 341 3 Cognate Elective 3Art 110 3 Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (400 level) 3Math Elective (300 or 400 level) 3 Cognate Elective 3Cognate Elective 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3



Catalogue Descriptions

The Department of Mathematics

The Department of Mathematics strives to prepare students for successful graduate study or a career in private industry, governmental service, or teaching.

Our mission is to expose the students of Morehouse College to a wide and balanced mathematical curriculum which includes a variety of areas. To accomplish this mission, we incorporate in our courses materials that motivate students and increase their abilities. We introduce students to a variety of applications of mathematics. We strive to produce students who are capable of reasoning abstractly and logically, and who are able to use technologies to solve real-world problems.

A student pursuing a major in mathematics is encouraged to choose a minor in one of a variety of areas in the physical, social, managerial, biological, chemical, computer, or engineering sciences in which mathematics is an essential tool.

Requirements for a Degree in Mathematics:

In order to qualify for a Bachelor of Science in Mathematics a student has a choice of following two distinct tracks. The B. S. degree (track I) is well suited for a student who plans to further his mathematical studies in graduate school. The B. S. (track II) degree is well suited for a student in the Dual Degree Program who plans to complete a major in Mathematics at Morehouse and a major in Engineering at another institution.

Under track I, a student must complete Mathematics 161, 162, 255, 263, 271, 361, 362, 371, 372, 497; he must complete either 321 or 341; and, he must complete 2 other 400 level or 1 other 300 level and one other 400 level (42 hours) mathematics courses. In addition, the student is required to complete six other mathematics or science courses from the approved cognate list. The six courses must include a three hour course in computer programming and one sequence (two courses) of other mathematics or science courses from the approved cognate course list (for example: Mathematics 341 & 342, Biology 111 & 112 or Computer Science 110 & 160) selected by the student in consultation with his advisor and that is approved by the department. Finally, the student may choose nine hours of mathematics or science cognate electives from the approved list of cognate electives for the B. S. A grade of “C” or better is required in all courses counted toward the degree. The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. S. in mathematics is 60 hours.

Under track II, a student must complete Mathematics 161, 162, 255, 263, 271, 321, 341, 361, 371, 497; he must complete either 362 or 372; and, he must complete 2 other mathematics courses at the 300 level or above (42 hours). In addition, the student is required to complete six other mathematics or science courses from the approved cognate list. The six courses must include a three hour course in computer programming and one sequence (two courses) of other mathematics or science courses from the approved cognate course list (for example: Mathematics 341 & 342, Biology 111 & 112 or Computer Science 110 & 160) selected by the student in consultation with his advisor and that is approved by the department. Finally, the student may choose nine hours of mathematics or science cognate electives from the approved list of cognate electives for the B. S. A grade of “C” or better is required in all courses counted toward the degree. The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. S. in mathematics is 60 hours.

In order to qualify for a Bachelor of Arts in Mathematics, a student must complete Mathematics 161, 162, 255, 263, 271, 361, 371, 497; he must complete either 321 or 341; he must complete either 362 or 372; and he must complete three other mathematics courses at the 300 or above level of which at least one must be at the 400 level (42 hours). In addition, the student is required to complete eighteen hours of cognate electives selected by the student in consultation with his advisor and approved by the chairman of the mathematics department. A three hour course in computer programming must be included in the eighteen hours of cognate electives. A grade of “C” or better is required in all courses counted toward the degree. The maximum number of semester hours of mathematics course work applied to the mathematics major is restricted to 54 hours. Thus, the total course load required for the B. A. in mathematics is 60 hours.

A student who has completed the degree requirements for a major in mathematics may also be recommended to receive departmental honours provided he qualifies for college honours, receives a grade of “B” or better in Math 497, and has an average of 3.0 or better in all mathematics courses taken in residence.

To qualify for a minor in mathematics, a student must complete the following mathematics course: Math 161, 162, 255, 263, and 271.


Approved list of cognate electives for the B. S. include; but, are not limited to:

Mathematics 321Mathematics 325Mathematics 327Mathematics 341Mathematics 342Mathematics 391Mathematics 398Mathematics 463Mathematics 465Mathematics 467Mathematics 475

Mathematics 485Mathematics 487Mathematics 498Biology 111Biology 112Biology 220Biology 251Biology 300 or aboveChemistry 111Chemistry 112Chemistry 211

Chemistry 231Chemistry 232Chemistry 300 or aboveComputer Science 110Computer Science 160Computer Science 260Computer Science 285Computer Science 300 or aboveEngineering 201

Engineering 205Engineering 206Engineering 300 or aboveEconomics 201Economics 202Economics 300 or abovePhysics 154Physics 253Physics 254Physics 300 or above

Course Sequence for Majors in Mathematics

Suggested pace for the B.S. (track I):Freshman YearMath 161, 162 plus core curriculum coursesSophomore YearMath 255, 263, 271 plus finish core curriculum coursesJunior Year361, 362, 371, 372, and 321 or 341 plus other science or mathematicsSenior Year497, two other 400 levels, or one other 300 level and one other 400 level plus other science or mathematics

Suggested pace for the B.S. (track II):Freshman YearMath 161, 162 plus core curriculum coursesSophomore YearMath 255, 263, 271 plus finish core curriculum coursesJunior Year321, 341, 361, 371, and 362 or 372 plus other science or mathematicsSenior Year497, two other 300 level or above mathematics courses plus other science or mathematics

Suggested pace for the B.A.:Freshman YearMath 161, 162 plus core curriculum coursesSophomore YearMath 255, 263, 271 plus finish core curriculum coursesJunior Year361, 371, 321 or 341, 362 or 372, and another 300 level math course plus cognate electivesSenior Year497, one other 300 or 400 level, and one other 400 level math course plus cognate electives


Model Plan of Study for B. S. in Mathematics Track I

Freshman Year


Sophomore Year


Junior Year

First Semester Second SemesterMath 361 3 Math 362 3Math 371 3 Math 372 3Math 321 or 341 3 Math or Science Cognate Elective 3Art 110 3 Math or Science Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (400 level) 3Math Elective (300 or 400 level) 3 Math or Science Cognate Sequence 3Math or Science Cognate Sequence 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3



Model Plan of Study for B. S. in Mathematics Track II

Freshman Year


Sophomore Year


Junior Year

First Semester Second SemesterMath 361 3 Math 341 3Math 371 3 Math 362 or 372 3Math 321 3 Math or Science Cognate Elective 3Art 110 3 Math or Science Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (300 or 400 level) 3Math Elective (300 or 400 level) 3 Math or Science Cognate Sequence 3Math or Science Cognate Sequence 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3



Model Plan of Study for B. A. in Mathematics

Freshman Year


Sophomore Year

First Semester Second SemesterMath 263 4 Math 271 3Math 255 3 Cognate Elective 3MFL 201 3 MFL 202 3English 250 3 Religion 201 3Edu 251 0 Physics 154 4HPED 154 1 Edu 252 0 total hours 14 total hours 16 60

Junior Year

First Semester Second SemesterMath 361 3 Math 362 or 372 3Math 371 3 Math Elective (300 or 400 level) 3Math 321 or 341 3 Cognate Elective 3Art 110 3 Cognate Elective 3Philosophy 261 3 English 253 3Edu 351 0 Edu 352 0 total hours 15 total hours 15 90

Senior Year

First Semester Second SemesterMath 497 3 Math Elective (400 level) 3Math Elective (300 or 400 level) 3 Cognate Elective 3Cognate Elective 3 Economics 201 3Biology 111 4 Free Elective 2Free Elective 3 Free Elective 3



Special College Core Curriculum Requirements: To satisfy the special college core curriculum requirements in oral communication effectiveness, each

mathematics major in consultation with his advisor will take one of the following courses: Principles of Speech Communication, Professional Communication, Communicating in Small Groups and Teams, Public Speaking, Argumentation and Debate, or Semantics. For a Bachelor of Science in Mathematics a student must take Biology 111 and either Physics 154 or Chemistry 111 to satisfy the college core curriculum requirement in science.

The College Core Curriculum is satisfied by successful completion of the sequence Math 100 & 110 (for students majoring in a program in the Division of Humanities), the sequence Math 100 & 120 (for students majoring in a program in the Division of Business and Economics or for students majoring in non-mathematics program in the Division of Science and Mathematics), Math 161 & 162 (for students majoring in Mathematics). Alternate satisfaction: sequence Math 110 & 130 (Division of Humanities); Math 120 & 160 (Division of Business and Economics); Math 130 & 160 (Division of Business and Economics); Math 120 & 157 (Division of Business and Economics or Division of Science and Mathematics (non-mathematics major)); Math 120 & 161 (Division of Business and Economics or Division of Science and Mathematics (non-mathematics major)); or, Math 161 & 162 (Division of Business and Economics or Division of Science and Mathematics). Any other sequence must be approved by the Department of Mathematics.

Morehouse College Department of Mathematics Course Offerings

090. Basic Mathematics. 3 hours.A review of intermediate algebra. Topics include arithmetic of natural numbers, integers, and real numbers; operations with algebraic expressions; exponents and radicals; linear equations and inequalities; and, quadratic equations and inequalities. (Institutional credit only)

100. College Algebra. 3 hours.A course designed to provide the student with the fundamental concepts of algebra which are essential for all higher mathematics courses. After completing this course, the student should understand the concepts and know how to apply the knowledge of algebraic equations and inequalities; functions and graphs; polynomial and rational functions; exponential and logarithmic functions; and, systems of equations and inequalities. Prerequisite: Math 090 with a “C” or better or mathematics placement.

110. Finite Mathematics. 3 hours.A course designed to provide the non-science/mathematics/engineering/business student an intense introduction to the foundations and fundamentals of mathematics for liberal arts majors. This course gives an introduction to many branches of mathematics and concentrates on pertinent and concrete examples and applications. After completing this course, the student should be able to work basic problems and word problems in linear algebra, logic, set theory, counting theory, probability, and statistics. Prerequisite: Math 100 with a “C” or better or mathematics placement.

120. Pre-calculus. 3 hours.Trigonometric functions; exponential and logarithmic functions; analytic geometry; mathematical induction; complex numbers; and the binomial theorem.Prerequisite: Math 100 with a “C” or better or mathematics placement.

130. Basic Statistics. 3 hours.A course designed to provide the student an intense foundational introduction to the fundamentals of statistics. The course includes an introduction to frequency of distribution and graphs; measures of central tendency; measures of variation; normal distribution; sampling; hypothesis testing; correlation; and linear regression. Also included is the use of some statistical packages (Excel, Minitab, SPSS, SAS, etc.). Prerequisite: Math 110 with a “C” or better or mathematics placement.


157. Principles of Mathematics. 3 hours.The Principles of Mathematics is a course designed to provide the student a strong foundation in the fundamentals of mathematics. Topics included are axiomatic logic; predicate calculus; syllogistic logic; basic logic proof techniques; axiom systems; the philosophy of mathematics; and, the first principle of mathematical induction. Also included are introductions to linear algebra; sets; combinatorics; probability; and, statistics. Emphasis is placed on logic and its role as one of the foundations of mathematics. Prerequisite: Math 120 with a “C” or better or mathematics placement.

160. Calculus for Business. 3 hours.A course designed to provide the business student a concentrated foundational introduction to the fundamentals of applied calculus. The course includes an introduction to both differential and integral calculus with a concentration in business applications.Prerequisite: Math 110 or Math 120 with a “C” or better or mathematics placement.

161. Calculus I. 4 hours.Calculus I is a first course in differential calculus and basic integral calculus. Topics included are limits, continuity, elementary transcendental functions, plane analytic geometry, differentiation, implicit differentiation, related rates, maxima and minima, the fundamental theorem of calculus, and introduction to definite integral with applications. Prerequisite: Math 120 with a “C” or better or mathematics placement.

162. Calculus II. 4 hours.Calculus II is a continuation of Math 161. Topics included are techniques and applications of integration, polar coordinates, parametric equations, infinite sequences and series, numerical integration, differential equations, L’Hôpital’s rule, and improper integration. Prerequisite: Math 161 with a “C” or better or mathematics placement.

211. Introduction to Discrete Mathematics. 3 hours.Discrete Mathematics is a course designed to provide the student an intense foundational introduction to “discrete” methods of mathematics. Topics included are logic; elementary set theory; algebraic structures; combinatorics; Boolean algebra; recurrence relations; and, graph theory. This course is primarily designed for students in computer science; but, students in other disciplines also benefit from a study of “discrete” methods as a complement to “continuous” methods. Prerequisite: Math 110 or Math 120 with a “C” or better.

255. Introduction to Set Theory. 3 hours.Introduction to Set Theory is a course designed to provide the student an introduction to the nature of mathematics and the use of proof. Topics included are a review of logic; reading, understanding, and constructing proofs; the first and second principle of mathematical induction, quantification, sets and their properties; axiomatics; product sets; relations; functions; cardinality; and, ordinality. Emphasis is placed on sets and their role as one of the foundations of mathematics. Prerequisites: Math 161 with a “C” or better.

263. Calculus III. 4 hours.Calculus III is a continuation of Math 162. Topics included are multivariable calculus, solid analytic geometry, linear approximation and Taylor's theorems, Lagrange multiples and constrained optimization, multiple integration and vector analysis including the theorems of Green, Gauss and Stokes; vector functions and curves in space, functions of several variables and partial derivatives. Prerequisite: Math 162 with a “C” or better.

271. Introduction to Linear Algebra. 3 hours.Topics included are matrices, determinants; simultaneous linear equations; vectors; linear transformations; matrix calculus; canonical forms; special matrices; applications to linear systems; least squares problems and, eigenvalues and eigenvectors. Prerequisite: Math 161 with a “C” or better.


321. Introduction to Ordinary Differential Equations. 3 hours.Ordinary Differential Equations Theory is a course designed to provide the student an introduction to mathematical formulation of physical problems in terms of ordinary differential equations, solutions to these equations, and physical interpretations of these solutions. Topics included are first order equations, nth order equations; numerical approximation techniques; Laplace transforms and systems of equations. Prerequisite: Math 162 with a “C” or better.

325. Applied Mathematics I. 3 hours.Applied Mathematics I is a course designed to provide the student an introduction to selected topics from convergence of infinite series and sequences; second order ordinary differential equations; uniform convergence; regions; Fourier series and integrals; eigenvalues and eigenfunctions; adjointness and boundary-value problems; and, Sturm-Liouville Theory. Prerequisites: Math 263 and Math 321 with a “C” or better.

327. Applied Mathematics II. 3 hours.Applied Mathematics II is a continuation of Applied Mathematics I. Topics include partial differential equations; conformal mappings applications to two-dimension potential problems; classification of second order partial differential equations; complex variables; integral equations; conformal mappings; Green’s functions; Legendre functions; Bessel functions; integral equations; wave motion; heat conduction; and L2 functions.Prerequisite: Math 325 with a “C” or better.

341. Probability and Statistics I. 3 hours.Probability and Statistics I is a course designed to provide the student an introduction to the mathematical theory of probability and statistics. Topics include the combinatorial analysis; axioms of probability; conditional probability; random variables; mass functions; distribution functions; discrete and continuous probability functions; marginal distributions; special distributions; joint distributions; and, properties of expectation. Prerequisites: Math 255 or Math 211; and, Math 162 with a “C” or better.

342. Probability and Statistics II. 3 hours.Probability and Statistics II is a continuation of Probability and Statistics I. Topics include random processes; the expected value; variance; covariance; correlation; conditional expectation; moment generating functions; Chebyshev’s Inequality; the Central Limit Theorem; estimation theory; bounding; hypothesis testing; analysis of variance; regression; parametric statistics; and, and non-parametric statistics. Prerequisite: Math 341 with a “C” or better.

361. Real Analysis I. 3 hours.The theory of single-variable calculus; elementary topology of the reals; limits; convergence; sequences; continuity; differentiability; and integrability. Prerequisites: Math 255 and Math 263 with a “C” or better. 362. Real Analysis II. 3 hours.Real Analysis II is a continuation of Real Analysis I. The theory of multi-variable calculus; series; transformations; uniform convergence; differentiation; and, integration. Prerequisites: Math 271 and Math 361 with a “C” or better.

371. Abstract Algebra I. 3 hours.Topics include groups; subgroups; cyclic groups; permutation groups; normal subgroups and quotient groups; homomorphisms; isomorphisms; and the fundamental isomorphism theorems; fundamental theorem of finite abelian groups; rings; integral domains; fields; subrings and ideals; quotient rings; ring homomorphism; and polynomial rings with coefficients in a field. Prerequisites: Math 255 or Math 211; and, Math 271 with a “C” or better.

372. Abstract Algebra II. 3 hours.Abstract Algebra II is a continuation of Abstract Algebra I. Topics include Sylow theorems; prime ideals; principal ideals and principal ideal domains; unique factorization domains; Euclidean domains; field extensions; and Galois Theory. Prerequisite: Math 371 with a “C” or better.


391. Special Topics in Mathematics. 3 hours.Designed to expose the student to areas of mathematics which are not part of the current curriculum, but are recognized as important to the field. Particular attention is focused on recent advances in mathematics. Prerequisites: Dependent on the subject.

398. Directed Reading. 1 hour.Student works with a faculty tutor who advises him in choice of material to be read. The student meets with the advisor frequently to discuss the topic studied. This course may be taken at most 3 times. Prerequisite: Math 255 and consent of instructor and department.

463. Real Variables. 3 hours.Topics include advanced theory of the reals; Lebesgue integration; metric spaces; Lp spaces; Banach spaces; measure theory; and, Borel sets. Prerequisite: Math 362 with a “C” or better.

465. Complex Variables. 3 hours.Topics include elementary properties of real and complex numbers; elementary topology in the complex plane; continuity, differentiability, and integrability of a complex variable; the Cauchy Theorem; Cauchy integral formula; elementary complex functions; complex sequences and series; Laurent and Taylor series; residue theory; and, contour integration. Prerequisite: Math 361 with a “C” or better.

467. Numerical Analysis. 3 hours.Topics include the basic concepts of numerical analysis; interpolation; finite differences; integration and approximation of orthogonal functions. Trigonometric interpolation; inverse interpolation; least squares; asymptotic representation; differential equations; continued fractions; and, linear programming. Prerequisites: Math 263, Math 271, and Math 321 with a “C” or better.

475. Number Theory. 3 hours.Topics include divisibility; Euclidean algorithm: primes; linear and quadratic congruences; arithmetic functions; primitive roots and indices; diophantine equations; and, cryptography. Prerequisite: Math 371 with a “C” or better.

485. Topology. 3 hours.Topics include metric spaces; pseudometrics; topologies; continuous functions; compactness; connectedness; continua; separation axioms; Moore spaces; Tychonoff spaces; Hausdorff spaces. Prerequisite: Math 361 with a “C” or better.

487. Differential Geometry. 3 hours.Topics include differential manifolds; tangent spaces; theory curves; torsion; the Frenet frame; directional forms; surfaces; tensor analysis; shape operators; orientation; and, intrinsic geometry. Prerequisite: Math 361 and Math 271 with a “C” or better.

497. Senior Seminar. 3 hours.The purpose of the seminar is to give the student experience in researching, writing, and presenting mathematical ideas and in listening critically to said ideas. Prerequisites: Math 361 and Math 371 with a “C” or better.

498. Directed Reading and Research. 1 hour.Student works with a faculty tutor who advises him in choice of material to be read and researched. The student meets with the advisor frequently to discuss and present the topic studied. This course may be taken at most 3 times. Prerequisite: Math 361, Math 371, or Math 398 and consent of instructor and department .


Motivation of Proposed ChangesThe Department of Mathematics at Morehouse College reviewed the catalogues at the college dating to 1976.

From this review, it was the opinion of the department that it was necessary to amend and enhance our offerings for both the Bachelor of Science and Bachelor of Arts degrees. Thus, the mathematics program has been revised so the Bachelor of Science and Bachelor of Arts have been retooled. The enclosed proposal allows our department to offer a mathematics program that is in accordance with many Departments of Mathematics in the United States.

In 1999, a special committee of the faculty was empanelled to research other mathematics programs. The committee compared the Morehouse College program with Kenyon College, Spelman College, Auburn University, Hampton University, Rensselaer Polytechnic Institute, Fisk University, Lincoln University, Bennett College, Reed College, Davidson College, Oberlin College, Columbia College, North Carolina A&T State University, Boston University, and Dartmouth College. These schools (hereafter referred to as the normative schools) are the schools that Morehouse used as benchmark schools for the 1998 reaccreditation by the Southern Association of Colleges and Schools (SACS).

The committee reviewed the Committee on the Undergraduate Program in Mathematics (CUPM) of the Mathematics Association of America (MAA) Reports of 1963 and 1965. The committee reviewed the CUPM discussion papers of 1979, 1989, 1992, and the draft 2001 update. The committee also investigated the standards of the American Mathematical Society (AMS), the Society of Industrial and Applied Mathematics (SIAM), and the National Science Board Committee on Undergraduate Science and Engineering Education (NSBCUSEE).

As part of the work of the committee, a survey was taken in 1999 of the mathematics faculty to gather information about our program, to garner a concurrence of opinion, and to get input from the faculty as to the future direction of our program. Not only was the faculty surveyed, but several alumni (1996 to the present) who majored in mathematics were given an opportunity to comment and respond to the document. Special attention was given to alumni of the program who were pursuing advanced degrees in the mathematical sciences.

In 2000, an accord was reached that the program needed to better prepare students for graduate work in the mathematical sciences but the program was adequately preparing students for successful completion of the Dual Degree.

The first concern is ameliorated by the revision of the major. The standards have not changed with regard to general course work [2, 3, 4, 5, 6, 7, 8]; but, emphasis has been placed on estimation in addition to proof. Thus, the department is meeting the general curricular standards. However, when the student progresses beyond the college introductory level the problems begin. It is important that the CUPM standards [2, 3] are followed which includes our Calculus I, II, III sequence and foundations course work. CUPM standards [2] and guidelines [4, 5, 6, 7, 8] outline minimal standards for successful graduate work include a year of real analysis, a year of abstract algebra, elementary linear algebra, ordinary differential equations, probability and statistics, computer programming, and a selection from the following: complex variables, differential geometry, numerical analysis, partial differential equations, number theory, combinatorics, operations research, applied mathematics, topology, advanced linear algebra, etc. The B. S. (track I) degree addresses the need for a breadth of experience in different disciplines within mathematics and a depth of experience in algebra and analysis. The B. S. (track II) degree allows students pursuing degrees in related sciences or the Dual Degree Program to major in mathematics and experience a breadth of different disciplines within mathematics. The B.A. (revised) maintains flexibility for the student who might decide to go to graduate school. In addition the B. A. (revised) better prepares the student for success in law school, teaching, or other fields by maintaining standards but allowing a student to design a course of study individual to the student’s interests and needs.

Principles of Mathematics would be converted to a three credit course from a two credit course. In 1997, some subject matter was added to Principles and some subject matter was expanded but the number of hours was not changed. Hence, the department opines that the course is a three hour course; but only two credits are awarded for successful completion. Also, by converting it to a three credit course it becomes a course a student can opt to take to fulfil the mathematics part of the college core curriculum requirement.

The point that the program was adequately preparing students for successful completion of the Dual Degree has been addressed by not changing the intended content of courses so as not to compromise the service the department performs for the dual degree program (see [13]).

Additionally, it should be noted that the B. S. and B. A. currently do not differ much. However, if approved, the proposal creates distinctions between the two degrees. The revised B. S. degree (track I) is well suited for a student who plans to further his mathematical studies in graduate school. It does not, however, only focus on said student. It is also well suited for a student who wishes to work in industry in the mathematical sciences or who wishes to pursue further study in other areas of science. The revised B. S. (track II) degree is well suited for a student in the Dual Degree Program who plans to complete a major in mathematics at Morehouse and a major in Engineering at another institution. It is also well suited for a student who wishes to work in industry in the mathematical sciences. The revised B.A. is well suited for a


student who wishes to study mathematics, law, philosophy, a social science, or other fields by maintaining standards but allowing a student the flexibility to design a course of study individual to the student’s interests and needs.

In revising and changing the program of study for both the Bachelor of Science and Bachelor of Arts degrees, the department is complying with the procedures, guidelines, and standards of CUPM. Positive results will result for our students, including a better system in which the students will adhere to prerequisites for courses. The revised numbering system streamlines the order of mathematics courses so that prerequisite course are denoted with numbers previous to another course, a course that should be taken in a particular year of a student’s matriculation is reflected in the first digit of the course, the content area is reflected in the second digit, and the sequence or lack thereof of content is reflected in the third digit. The department believes that a student “on task” will be able to complete his requirements for graduation in four years and give him proper reference during matriculation. The numbering system and prerequisite ordering was painstakingly revised, changed, discussed, revised again, etc. It represents an exceedingly better system than the present prerequisite system.

Consonance of Proposed Changes The faculty of the Mathematics Department is in agreement with the proposed changes. With the proposed

changes in our current program, the faculty is committed to continue to provide opportunities for our students to hone their skills in the following areas: critical thinking; analytic and technical reasoning; and, oral and written communication. The Department of Mathematics will continue to prepare students for a career in the private or public sector or graduate study in all fields, including the mathematical sciences and all areas of mathematics education.

Further, the proposed changes are designed to increase the number of mathematics majors who choose to pursue further study in the mathematical sciences and better prepare them for further study. The Chronicle of Higher Education reported that during the 1990s the number of African-American men who completed a Ph.D. in mathematics was on average five or six per year. The faculty of the Department of Mathematics is committed to increase these numbers. If our program can establish a record of sending between three and six students per year to graduate school, conservatively assuming that half of those men go on past the Master’s degree, our program can be in the position of increasing the number of African-American men who complete a Ph.D. in mathematics by approximately fifty percent. This goal is not only consonant with the department’s goals, but with the division’s goals and the college’s mission of producing outstanding leaders in all fields. In the field of mathematics, if all goes well, we can be responsible for a major change in the face, character, and focus of the mathematical world.

Additional Resource Requirements No additional resources from the college are necessary to implement the changes proposed herein. The changes

proposed represent more focus on mathematics and science for mathematics majors. The changes proposed do not require an increase in the number of mathematics faculty.

Funding Sources No additional funding specific for the changes to the mathematics major herein outlined is anticipated from the

College. Already mentioned were some of the funding sources anticipated to support some of the changes. In addition to the CEM grant, there are funding sources both government and private that can be tapped. For example, the National Science Foundation (NSF), the Department of Education (DOE), the Office of Naval Research (ONR), the Department of Defence (DOD), and several trusts and foundations have a track record of providing funds for the improvement of education access, opportunity, and outcomes when grants are properly drafted to address such issues. After the division and the college approve the revisions to the major, the faculty of the mathematics department can act to draft proposals for funding from external sources to meet the needs of implementing, monitoring, revising (if applicable), and reporting the results of the changes.


References1. Conference Board of the Mathematical Sciences, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States, Washington, DC, Mathematical Association of America and the American Mathematical Society, 1995.

2. Committee on the Undergraduate Program in Mathematics, Pre-graduate Preparation of Research Mathematicians, Washington, DC, Mathematical Association of America, 1963.

3. Committee on the Undergraduate Program in Mathematics, A General Curriculum in Mathematics for College, Washington, DC, Mathematical Association of America, 1965.

4. Committee on the Undergraduate Program in Mathematics, Reshaping College Mathematics, Washington, DC, Mathematical Association of America, 1989.

5. Committee on the Undergraduate Program in Mathematics, The Undergraduate Major in the Mathematical Sciences, Washington, DC, Mathematical Association of America, 1992.

6. Committee on the Undergraduate Program in Mathematics, CUPM Discussion Papers about the Mathematical Sciences in 2010: What Should Students Know? (Working Paper), Washington, DC, Mathematical Association of America, 2001.

7. Committee on the Undergraduate Program in Mathematics, Guidelines for Programs and Departments in Undergraduate Mathematical Sciences (Working Paper), Washington, DC, Mathematical Association of America, 2001.

8. Committee on the Undergraduate Program in Mathematics, CUPM Interim Reports: Toward a Working Draft Curriculum Guide (Working Paper), Washington, DC, Mathematical Association of America, 2001.

9. Morehouse College, Catalogue 1976-1977, Atlanta, GA, Morehouse College, 1976.




13. National Science Board Committee on Undergraduate Science and Engineering Education, Undergraduate Science, Mathematics, and Engineering Education, Washington, DC, National Science Board, 1986.

End of proposal

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