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
321 Mathematics
325 Mathematics
327 Mathematics
341 Mathematics
342 Mathematics
391 Mathematics
398 Mathematics
463 Mathematics
465 Mathematics
467 Mathematics
475 |
Mathematics
485 Mathematics
487 Mathematics
498 Biology
111 Biology
112 Biology
220 Biology
251 Biology 300 or
above Chemistry
111 Chemistry
112 Chemistry 211 |
Chemistry
231 Chemistry
232 Chemistry 300 or
above Computer Science
110 Computer Science
160 Computer Science
260 Computer Science
285 Computer Science 300 or
above Engineering
201 |
Engineering
205 Engineering
206 Engineering 300 or
above Economics
201 Economics
202 Economics 300 or
above Physics
154 Physics
253 Physics
254 Physics 300 or
above |
Suggested
pace for the B.S. (track I):
Math
161, 162
plus core curriculum courses
Math
255, 263, 271
plus finish core curriculum courses
361,
362, 371, 372, and 321 or 341
plus other science or mathematics
Senior
Year
497,
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):
Math
161, 162
plus core curriculum courses
Math
255, 263, 271
plus finish core curriculum courses
321,
341, 361, 371, and 362 or 372
plus other science or mathematics
Senior
Year
497,
two other 300 level or above mathematics courses
plus other science or mathematics
Math
161, 162
plus core curriculum courses
Math
255, 263, 271
plus finish core curriculum courses
361,
371, 321 or 341, 362 or 372, and another 300 level math course
plus cognate electives
Senior
Year
497,
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
Math
161
4
Math 162
4
English
101
3
CSC 110 (Programming Cognate)
3
History
111
3
English 102
3
Music
111
3
History 112
3
Edu
151
0
Psychology 101
3
Edu
153
0
Edu 152
0
HPED
151
1
Edu 154
0
total hours
14
total hours
16
30
Sophomore
Year
Math
263
4
Math 271
3
Math
255
3
Math or Science Cognate Elective 3
MFL
201
3
MFL 202
3
English
250
3
Religion 201
3
Edu
251
0
Physics 154
4
HPED
154
1
Edu 252
0
total hours
14
total hours
16
60
Junior
Year
Math
361
3
Math 362
3
Math
371
3
Math 372
3
Math
321 or 341
3
Math or Science Cognate Elective 3
Art
110
3
Math or Science Cognate Elective 3
Philosophy
261
3
English 253
3
Edu
351
0
Edu 352
0
total hours
15
total hours
15
90
Senior
Year
Math
497
3
Math Elective (400 level)
3
Math
Elective (300 or 400 level)
3
Math or Science Cognate Sequence
3
Math
or Science Cognate Sequence 3
Economics 201
3
Biology
111
4
Free Elective
2
Free
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
Math
161
4
Math 162
4
English
101
3
CSC 110 (Programming Cognate)
3
History
111
3
English 102
3
Music
111
3
History 112
3
Edu
151
0
Psychology 101
3
Edu
153
0
Edu 152
0
HPED
151
1
Edu 154
0
total hours
14
total hours
16
30
Sophomore
Year
Math
263
4
Math 271
3
Math
255
3
Math or Science Cognate Elective 3
MFL
201
3
MFL 202
3
English
250
3
Religion 201
3
Edu
251
0
Physics 154
4
HPED
154
1
Edu 252
0
total hours
14
total hours
16
60
Junior
Year
Math
361
3
Math 341
3
Math
371
3
Math 362 or 372
3
Math
321
3
Math or Science Cognate Elective 3
Art
110
3
Math or Science Cognate Elective 3
Philosophy
261
3
English 253
3
Edu
351
0
Edu 352
0
total hours
15
total hours
15
90
Senior
Year
Math
497
3
Math Elective (300 or 400 level)
3
Math
Elective (300 or 400 level)
3
Math or Science Cognate Sequence
3
Math
or Science Cognate Sequence 3
Economics 201
3
Biology
111
4
Free Elective
2
Free
Elective
3
Free Elective
3
total hours
16
total hours
14
120
Model
Plan of Study for B. A. in Mathematics
Freshman
Year
Math
161
4
Math 162
4
English
101
3
CSC 110 (Programming Cognate)
3
History
111
3
English 102
3
Music
111
3
History 112
3
Edu
151
0
Psychology 101
3
Edu
153
0
Edu 152
0
HPED
151
1
Edu 154
0
total hours
14
total hours
16
30
Sophomore
Year
Math
263
4
Math 271
3
Math
255
3
Cognate Elective
3
MFL
201
3
MFL 202
3
English
250
3
Religion 201
3
Edu
251
0
Physics 154
4
HPED
154
1
Edu 252
0
total hours
14
total hours
16
60
Junior
Year
Math
361
3
Math 362 or 372
3
Math
371
3
Math Elective (300 or 400 level)
3
Math
321 or 341
3
Cognate Elective
3
Art
110
3
Cognate Elective
3
Philosophy
261
3
English 253
3
Edu
351
0
Edu 352
0
total hours
15
total hours
15
90
Senior
Year
Math
497
3
Math Elective (400 level)
3
Math
Elective (300 or 400 level)
3
Cognate Elective
3
Cognate
Elective
3
Economics 201
3
Biology
111
4
Free Elective
2
Free
Elective
3
Free Elective
3
total hours
16
total hours
14
120
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.
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 .