*Course Description:* Fundamental concepts and theorems of mathematics

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* None

*Semester/s Offered:* First Semester

**MATH 26. Analytic Geometry and Calculus I**

*Course Description:* Straight lines, functions and graphs; limits and continuity; concepts of derivatives; derivatives of algebraic functions; differential applications of curve sketching; related rates; maxima and minima problems; equations of the second degree; indefinite integral and its applications; area under the curve; definite integral

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 14 or MATH 17

*Semester/s Offered:* First Semester, Second Semester, Midyear

**MATH 27. Analytic Geometry and Calculus II **

*Course Description:* Differentiation and integration of transcendental functions. Indeterminate forms; integration formulas. Integration procedures. Application of integration. Polar coordinate system

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 26

*Semester/s Offered:* First Semester, Second Semester, Midyear

**MATH 28. Analytic Geometry and Calculus III**

*Course Description:* Parametric equations, vectors and solid analytic geometry; partial differentiation; multiple integrals; infinite series

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 27

*Semester/s Offered:* First Semester, Second Semester, Midyear

**MATH 36. Mathematical Analysis I**

*Course Description:* The real number system; plane analytic geometry and conic sections, limits and continuity, differentiation and integration of algebraic functions

*Course Credit:* 5 units (5 hrs (class))

*Prerequisite:* MATH 14 or MATH 17

*Semester/s Offered:* First Semester, Second Semester

**MATH 37. Mathematical Analysis II**

*Course Description:* Derivatives and integrals of transcendental functions; parametric equations; polar coordinates, techniques of integration and applications; vectors in two and three dimensions; loci in space

*Course Credit:* 5 units (5 hrs (class))

*Prerequisite:* MATH 36

*Semester/s Offered:* First Semester, Second Semester

**MATH 38. Mathematical Analysis III**

*Course Description:* Theories, techniques and applications of partial differentiation and multiple integration, vector differential and integral calculus; elements of infinite series

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 37

*Semester/s Offered:* First Semester, Second Semester

**MATH 101. Logic and Set Theory**

*Course Description:* Elements of mathematical logic and the algebra of propositions; arguments, set operations, functions and relations; algebra of sets; cardinal and ordinal numbers; ordered sets; axiom of choice and other topics in set theory

*Course Credit:* 3 units (5 hrs (2 class, 3 lab))

*Prerequisite:* AMAT 19 or MATH 20 and MATH 26 or MATH 36

*Semester/s Offered:* First Semester, Second Semester

**MATH 103. Elementary Theory of Numbers**

*Course Description:* Divisibility of integers; primes; congruences; quadratic reciprocity; some functions in number theory and diophantine equations

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 101

*Semester/s Offered:* Second Semester

**MATH 111. Modern Algebra I**

*Course Description:* Binary operations and groups; subgroups; groups of permutations; cyclic groups; isomorphism, homomorphism; cosets and factor groups

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 101

*Semester/s Offered:* First Semester

**MATH 112. Modern Algebra II**

*Course Description:* Rings, fields and integral domains, ideals and quotient rings, polynomial fields, automorphisms, selected topics

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 111

*Semester/s Offered:* Second Semester

**MATH 120. Linear Algebra**

*Course Description:* Solution of system of linear equations by matrices; matrix operations and vector spaces; linear operators and linear transformation; determinants and eigenvalues

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 37 and MATH 101 or COI

*Semester/s Offered:* First Semester, Second Semester

**MATH 130. Metric Geometry**

*Course Description:* Foundation and structure of metric geometry as a postulational system of reasoning

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 101

*Semester/s Offered:* Second Semester

**MATH 133. Non-Euclidean Geometries**

*Course Description:* Origin and development of non-Euclidean geometries

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 130

*Semester/s Offered:* First Semester

**MATH 135. Projective Geometry**

*Course Description:* Synthetic and analytic treatment of projective transformations, duality, conics, polarities and involution; axiomatic projective geometry; extensions of real projective geometry

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 133 or COI

*Semester/s Offered:* Second Semester

**MATH 141. Introductory Combinatorics**

*Course Description:* Elementary configurations; enumeration of configurations and investigation of unknown configurations

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 and either MATH 101 or CMSC 56 and CMSC 57

*Semester/s Offered:* First Semester

**MATH 143. Graph Theory**

*Course Description:* Path problems, directed graphs and colorability and their application

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 101 or CMSC 56 and CMSC 57

*Semester/s Offered:* First Semester

* *

**MATH 151. Ordinary Differential Equations**

*Course Description:* Theory methods and applications of ordinary differential equations

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 or MATH 28

*Semester/s Offered:* First Semester

**MATH 152. Partial Differential Equations**

*Course Description:* Theory, methods and applications of partial differential equations

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 151

*Semester/s Offered:* Second Semester

**MATH 155. Advanced Calculus I**

*Course Description:* Geometry of the euclidean n-space; topological concepts; sequences; continuity; limits; convergence

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 and MATH 101 or COI

*Semester/s Offered:* First Semester

**MATH 156. Advanced Calculus II**

*Course Description:* Transformation; differentiation of composite functions; inverses of functions and transformations; integration-definite integral, improper integral

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 155

*Semester/s Offered:* Second Semester

**MATH 160. Vector Analysis**

*Course Description:* The algebra of vectors; differentiation of vectors; the vector operators del and curl; divergence; Frenet-Serret formulas; involutes, envelopes, first and second fundamental forms; geodesics, integration of vectors

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 or MATH 28

*Semester/s Offered:* Second Semester

**MATH 165. Complex Analysis I**

*Course Description:* Properties of complex numbers; topological concepts in the complex plane; limits and sequences; analytic and elementary functions; complex differentiation and integration; integral formulas and related theorems

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 and MATH 101 or COI

*Semester/s Offered:* First Semester

**MATH 166. Complex Analysis II**

*Course Description:* Generalization of the theories and techniques of power series, integration and transformation to complex variables

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 165

*Semester/s Offered:* Second Semester

**MATH 168. Introductory Topology**

*Course Description:* Basic topological concepts, theory and methods

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 and MATH 101

*Semester/s Offered:* Second Semester

* *

**MATH 170. Finite Differences**

*Course Description:* Calculus of finite differences; difference equations in general; and linear difference equations with constant coefficients and selected topics

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38

*Semester/s Offered:* First Semester

**MATH 174. Numerical Analysis I**

*Course Description:* Theory, analysis and implementation of algorithms in polynomial approximation, numerical differentiation and integration

*Course Credit:* 3 units (5 hrs (2 class, 3 lab))

*Prerequisite:* MATH 38 and either AMAT 150 or CMSC 21

*Semester/s Offered:* First Semester

**MATH 175. Numerical Analysis II**

*Course Description:* Theory, analysis and implementation of algorithms for solving non-linear equations, linear systems and ordinary differential equations

*Course Credit:* 3 units (5 hrs (2 class, 3 lab))

*Prerequisite:* MATH 174

*Semester/s Offered:* Second Semester

**MATH 181. Introduction to Probability Theory**

*Course Description:* Elements of combinatorial analysis and introductory probability theory

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 101 and MATH 38 or MATH 28

*Semester/s Offered:* First Semester

**MATH 182. Introduction to Stochastic Processes**

*Course Description:* Theory and applications of Bernoulli trials; infinite sequence of trials; random walk and run problems; branching processes and Markov chains

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 181 or STAT 143

*Semester/s Offered:*

**MATH 190. Special Problems**

*Course Description:* Maybe taken twice provided the total number of units to be credited to the student’s program will not exceed 4 units

*Course Credit:* 3 units

*Prerequisite:* COI

*Semester/s Offered:* First Semester, Second Semester, Midyear

**MATH 191. Special Topics**

*Course Description:* May be taken twice provided that total number of units to be credited to the student’s program will not exceed 4 units

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* COI

*Semester/s Offered:* Second Semester

**MATH 192. Foundations of Mathematics**

*Course Description:* Axiomatic methods and theories; symbolic logic calculi; school mathematics reform theses; constructivistics, formalistics and related mathematics; various schools of mathematical thought and operationality of their theses

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* COI

*Semester/s Offered:* Second Semester

**MATH 195. Research Methods in Mathematics**

*Course Description:* Principles governing mathematical research and documentation

*Course Credit:* 3 units (3 hrs (class))

*Prerequisite:* MATH 38 and MATH 101

*Semester/s Offered:* First Semester, Second Semester

** **

**MATH 199. Undergraduate Seminar**

*Course Description:* May be taken twice

*Course Credit:* 1 units (1 hr (class))

*Prerequisite:* COI

*Semester/s Offered:* Second Semester

**MATH 200. Undergraduate Thesis**

*Course Description:* May be taken twice

*Course Credit:* 6 units

*Prerequisite:* COI

*Semester/s Offered:* First Semester, Second Semester, Midyear