These are the Undergraduate Courses of the Institute of Mathematics.

 

COURSE NO. DESCRIPTION SYLLABUS
Math 1 

General Mathematics
The development of mathematical literacy and appreciation through a synoptic view of the different branches of mathematics with historical notes and applications.

Credit: 3 u.

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 Math 2

Practical Mathematics
Basic mathematical skills and applications in everyday life.

Credit: 3 u.

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Math 11

College Algebra
Linear equations; algebraic and graphical solutions of the quadratic equations; exponents and radicals; complex numbers; binomial expansion; determinants; progressions; solutions of equations, several equations in several variables.

Prerequisite: one year of high school algebra

Credit: 3 u.

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Math 14

Plane Trigonometry
Logarithms; graphs of the trigonometric functions; the general triangle; solutions of trigonometric, inverse trigonometric, exponential and logarithmic equations; complex numbers.

Prerequisite: one year each of high school algebra and plane geometry

Credit: 3 u.

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Math 17

Algebra and Trigonometry
Sets and numbers; the algebra of numbers as logical system; inequalities; absolute values and coordinates systems; functions and graphs; circular, linear, quadratic, and polynomial functions; exponential and logarithmic functions; applications of the circular functions to angles.

Prerequisite: one year of high school algebra

Credit: 5 u.

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Math 53

Elementary Analysis I
Functions and their graphs; limits and continuity; the derivative; derivatives of algebraic and trigonometric functions; exponential and logarithmic functions; inverse functions; antiderivatives and definite integrals; fundamental theorem of calculus; applications of the definite integral.

Prerequisite: Math 17 or equivalent

Credit: 3 u.

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Math 54

Elementary Analysis II
Integration methods; applications of the definite integral; plane and solid analytic geometry; polar coordinates; vectors; parametric equations. Sequences and series; power series.

Prerequisite: Math 53

Credit: 5 u.

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Math 55

Elementary Analysis III
Partial differentiation; multiple integrals; infinite series; differential equations.

Prerequisite: Math 54 or equivalent

Credit: 3 u.

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Math 60

Precalculus
Algebraic operations, functions, analytic, geometry, trigonometry, matrices.

Prerequisite: none

Credit: 5 u.

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Math 63

Calculus I
Functions of a single variable; limits; continuity; the derivative and the Riemann integral; derivatives of algebraic, trigonometric and inverse trigonometric functions; applications; polar coordinates; conic sections.

Prerequisite: Math 60 or equivalent

Credit: 5 u.

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Math 64

Calculus II
The exponential, logarithmic and hyperbolic functions; techniques of integration; vectors and vector-valued functions; improper integrals; infinite series; power series; applications.

Prerequisite: Math 63 or equivalent

Credit: 5 u.

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Math 65

Calculus III
Calculus of several variables and Fourier series.

Prerequisite: Math 64

Credit: 3 u.

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Math 100

Introduction To Calculus
Limits; derivatives; integrals; applications.

Prerequisite: Math 17 or consent of instructor

Credit: 4 u.

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Math 102

Intermediate Calculus
Integration techniques; multivariate calculus; sequences and series; introduction to matrices; applications to economics, business, life and social sciences.

Prerequisite: Math 100 or equivalent, or Math 53 or equivalent

Credit: 3 u.

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Math 109

Fundamental Concepts Of Mathematics
Algebra of sets and logic; methods of proof; functions and relations; logical nature and structure of mathematics; introduction to number-theory; algebra arid geometry of complex numbers.

Prerequisite: 2nd year standing

Credit: 3 u.

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Math 110.1

Abstract Algebra I
Algebraic relations, lattices, Boolean algebra; groups; rings; integral domain.

Prerequisite: Math 109

Credit: 3 u.

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Math 110.2

Abstract Algebra II
Fields; vector spaces; linear transformations; matrices; characteristic values; diagonalization; inner product; quadratic forms.

Prerequisite: Math 110.1

Credit: 3 u.

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Math 110.3

Abstract Algebra III
Fields of quotients of integral domains; polynomial rings; field extensions; Galois theory; other systems.

Prerequisite: Math 110.1

Credit: 3 u.

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Math 114

Linear Algebra
Vector spaces; linear transformations; matrices; eigenvalues; canonical forms; orthogonality; applications.

Prerequisite: Math 54 or equivalent

Credit: 3 u.

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Math 117 *

Elementary Theory Of Numbers
Properties of integers; divisibility; unique factorization theorem; solutions of congruences; residue systems; primitive roots and the quadratic reciprocity law; solutions of Diophantine equations.

Prerequisite: Math 109 or COI

Credit: 3 u.

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Math 121

Elementary Differential Equations
Ordinary differential equations of order one; linear differential equations; differential operators; Laplace Transform; nonlinear equations; series solutions about an ordinary point.

Prerequisite: Math 54 or equivalent

Credit: 3 u.

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Math 122

Differential Equations And Applications
Modeling systems; solutions of ordinary differential equations (ODE's) of order one and systems of ODE's Laplace transform; solutions of the classical partial differential equations; numerical methods.

Prerequisite: Math 65 or equivalent

Credit: 3 u.

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Math 123.1

Advance Calculus I
The real number system; point set topology sequence of real numbers; limits and continuity; metric spaces; the derivative; the Riemann integral; series of real numbers; sequence and series of functions; uniform convergence; power series.

Prerequisite: Math 65 or equivalent

Credit: 3 u.

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Math 123.2

Advance Calculus II
Topology of Rn; continuity and derivative; Taylor's formula; implicit and inverse function theorems; analytic geometry of curves and surfaces; Serret-Frenet formula; multiple integration; improper integrals; transformation; metric and normed spaces.

Prerequisite: Math 123.1

Credit: 3 u.

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Math 126 *

Real Analysis
Properties of real numbers; integral of step functions; Lebesgue integral; convergence theorems; measureable functions; measurable sets; selected topics.

Prerequisite: Math 123.1

Credit: 3 u.

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Math 128

Complex Analysis
Analytic functions; elementary functions; complex integration; power series; residues; conformal mapping.

Prerequisite: Math 109 or equivalent, and Math 123.1

Credit: 3 u.

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Math 131 *

Elementary Set Theory
Axioms of Set Theory; relations and functions; natural numbers; cardinal numbers and the Axioms of Choice; ordering and ordinals.

Prerequisite: Math 110.1

Credit: 3 u.

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Math 140

Introduction To Modern Geometries
Development of modern geometries; finite geometries; geometric transformations; projective geometry; non-Euclidean geometries.

Prerequisite: Math 109 or equivalent

Credit: 3 u.

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Math 142 *

Elementary Topology
Topologies and topological spaces; functions and homeomorphisms; continuity; metric spaces; compactness and connectedness.

Prerequisite: Math 123.1 or consent of instructor

Credit: 3 u.

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Math 146 **

Introduction To Differential Geometry
Elementary topology; calculus of several variables, curves and surfaces; Strokes and Gauss theorem; differential forms.

Prerequisite: Math 65 or equivalent

Credit: 3 u.

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Math 147 **

Introduction To Algebraic Geometry
Projective varieties; algebraic and elliptic curves.

Prerequisite: Math 110.1 and Math 140

Credit: 3 u.

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Math 148 **

Introduction To Projective Geometry
Projective planes and spaces.

Prerequisite: Math 110.1 & Math 140

Credit: 3 u.

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Math 150.1

Mathematical Statistics I
Combinatorial probability; probability of distributions; joint and conditional distributions; random variables; distributions of functions of random variables; mathematical expectation; moment-generating functions; sampling distributions.

Prerequisite: Math 65 or equivalent, and Stat 101

Credit: 3 u.

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Math 150.2 *

Mathematical Statistics II
Limiting distributions; estimation of parameters; tests of hypothesis; regression and correlation; analysis of variances; applications.

Prerequisite: Math 150.1

Credit: 3 u.

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Math 157

Discrete Mathematical Structures
Fundamentals of set theory; algebraic relations;combinatorial algorithms; algebraic structures and their applications in computer science.

Prerequisite: Math 54

Credit: 3 u.

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Math 162 *

Theory Of Interest
Simple interest; compound interest; continuous interest; annuities; amortization schedules and sinking funds; bonds and other securities; special topics.

Prerequisite: consent of instructor

Credit: 3 u.

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Math 164 *

Mathematics of Life Contingencies
Mathematical theory of life contingencies involving single-life functions; mortality; life annuities and insurances; reserves; the expense factor; population theory.

Prerequisite: Math 150.1 & 162

Credit: 3 u.

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Math 171

Introduction To Numerical Analysis
Error analysis; solution of a single non-linear equation; solution of systems of equations; solution of ordinary differential equations; series.

Prerequisite: Math 110.2 or equivalent, and Math 122 or equivalent (2lec, 3lab)

Credit: 3 u.

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Math 180.1 *

Operations Research I
Review of classical optimization theory; introduction to linear programming; quadratic programming, non-linear programming and dynamic programming; networks (Path, PERT/CPM) and inventory problems.

Prerequisite: Math 114 or equivalent

Credit: 3 u.

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Math 180.2 *

Operations Research II
Review of probability theory; Stochastic models; Markov chains; introduction to queueing theory; introduction to simulation; games, replacement and reliability theory.

Prerequisite: Math 180.1 and Math 150.1

Credit: 3 u.

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Math 196 *

Undergraduate Seminar

Prerequisite: Junior Standing

Credit: 1 u.

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Math 197 *

Special Topics

may be taken at most thrice provided topics are different; topics to be specified

Prerequisite: consent of instructor

Credit: 3 u.

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Math 200

Undergraduate Thesis

Prerequisite: Senior Standing

Credit: 3 u.

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* possible Math elective for Math majors
** possible Geometry or Math elective for Math majors