Math 11 College Algebra (3 units)

Fundamental Operations, basic theorems and principles, axioms of the real number system, factoring, exponents, radicals, ratio and proportion, equations, functions and relations, inequalities, applications through problem?solving.

Math 12 Plane Trigonometry (3 units)

Cartesian Coordinate System, trigonometric functions, solution of right triangles, course and bearing, graphs of trigonometric functions, inverse trigonometric functions, trigonometric equations, oblique triangles.

Math 14 Solid Mensuration (3 units)

Review of plane geometry. Measurement of surface areas and volume of the different geometric solids.

Math 16 Applied General Statistics and Demography (3 units)

Nature of statistics, permutations, combinations, probability, sampling procedures, collection and presentation of data. Interpretation of the normal curve, linear correlation and regression. Introduction to statistical inference. Study of population growth. (PR Math 11)

Math 22 Advanced College Algebra (3 units)

Geometry of real numbers, functions and their graphical representation, linear and quadratic functions, matrices and determinants, polynomial functions, permutation, combination, and probability, binomial theorem, mathematical induction, exponential and logarithmic functions, complex numbers and vectors. (PR Math 11)

Math 25 Introduction to College Geometry (3 units)

Foundations of geometry and basic Euclidean geometry. Valuable to those who expect to teach secondary school geometry.

Math 28 Mathematical Analysis I (5 units)

Functions and their graphs, Operations on functions, Functions as mathematical models, Limit if a function, definitions and theorems, Continuity of a function at a number, Derivative of a function, Theorems on differentiation of algebraic functions and higher derivatives, Rectilinear motion, Derivatives of Trigonometric Functions, Related Rates, Maximum and minimum function values, Applications involving an absolute extremum , sketching graphs of functions and their derivatives, Differentials, Antidifferentiation, Definite Integral and the Fundamental Theorem of Calculus, Area of plane region, Volumes of solids by slicing, disks, and washers, Volume of solids by cylindrical shell. (PR Math 11, Math 12)

Math 32 Linear Algebra (3 units)

Matrices, Properties of Matrix operations, Inverse of a matrix, Positive definite matrices, Square root of a matrix, Determinants, Cramer’s Rule, Vectors and Vector spaces, Subspaces, Linear independence/dependence, Basis and Dimensions, Rank of a matrix, Linear transformations, Eigenvalues and eigenvectors. (PR Math 11)

Math 33 Mathematical Analysis II (5 units)

Logarithmic and Exponential Functions, Inverse Trigonometric Functions, Hyperbolic Functions, Length of Arc, Center of Mass and centroid of a plane region, Work, Force due fluid pressure, Integration by Parts, Trigonometric Integrals, Trigonometric Substitution, Integration of Rational Functions and logistic growth, Integration by other substitution techniques, Indeterminate forms, Improper integrals. (PR Math 28)

Math 34 Foundations and history of Mathematics (3 units)

Early development on the foundations of mathematics, schools of thought on the origin and nature of mathematics, mathematical systems, Zermelo?Fraenkl Set Theory, Survey on the development of mathematics from Plato to Lakatos. (PR Philo 31)

Math 35 Abstract Algebra 1 (3 units)

Groups, Subgroups, Cyclic groups, Cosets, Homomorphisms, isomorphism, Cayley’s Theorem, Factor Groups, Sylow Theorems, Rings, Fields Integral Domains, Rings of Polynomials, Polynomials over a field, Factor rings, ldeals. (PR Math 11)

Math 38 Mathematical Analysis III (5 units)

Vectors in Three?Dimensional Space, Operations on vectors: The dot and cross products, Planes and Lines in R3, Surfaces, Vector?valued functions and curves, Calculus of vector?valued functions, Curvature, Curvilinear Motion, Differential Calculus of functions of more than one variable, Multiple Integration, Vector Fields, Line Integrals, Green’s Theorem, Surface Integrals, Gauss Divergence Theorem, Stoke’s Theorem. (PR Math 33)

Math 41 Differential Equations (3 units)

Equations of order one, existence theorem, separation of variables, homogeneous functions, exact equations, linear equations of order one, integrating factors, Bernoulli’s equations, non?elementary integrals, general solution of homogeneous equations, linear coefficients with constant coefficients, variation of parameters, inverse differential operators, Laplace transforms, linear systems. Applications. (PR Math 33)

Math 42 Differential Equations II (3 units)

Linear Systems of Equations, Electric Circuits and Networks, Nonlinear Equations, Power Series Solutions, Solutions of Near Regular points, Equations of Hypergeometric Type, Numerical Methods, Partial Differential Equations, Orthogonal Sets, Fourier Series, Boundary Value Problems. (PR Math 41)

Math 44 Graph Theory (3 units)

Basic concepts, Cyclomatic number, Trees and Arborescences, Paths, centres and diameters, Flow problems, Degrees and Demi?degrees, Matching, Stability number, Kernels and Grundy functions, Chromatic number, Perfect graphs. (PR Math 22)

Math 45 Teaching Methods in Mathematics (3 untis)

Use of principles of teaching learning associated with instructional operations in mathematics, selection and application of teaching strategies appropriate for particular math topic, bulletin boards. (4th Year Level)

Math 46 Complex Variables (3 units)

Complex numbers and geometrical representations, Point sets, sequences, and mappings, Analytic Functions, Elementary Functions, Integration, Contour Integration, Simple Closed Contours, Cauchy Integral Theorems, Morera’s Theorem, Cauchy’s Inequality, Liouville’s Theorem, Power Series, Calculus of Residues, Conformal Representation. (PR Math 38)

Math 47 Abstract Algebra II (3 units)

Rings: integral domains, quaternions as a division ring, homomorphisms, ideals, factor rings, fields. Fields: Axioms and elementary theorems, finite fields, solutions of polynomial equations, field extensions. (PR Math 35)

Math 49 Advanced Calculus I (3 units)

Sets and Functions, Topological Terminologies, Monotonic Sequences, Compact sets, Continuity, uniform continuity, Limits of functions on Rn, Taylor’s Theorem. (PR Math 38)

Math 50 Advanced Calculus II (3 units)

Definite integral, improper integrals, differentials of functions and transformations, implicit function theorems. (PR Math 49)

Math 52 Real Analysis (3 units)

Set theory, real number system, measurable sets, Lebesgue measure, Non?measurable sets, measurable functions, Riemann integral, Lebesgue Integral, convergence in measure, differentiation of an integral, absolute continuity. (PR Math 38)

Math 54 Numerical Analysis (3 units)

Cramer’s rule, Gauss?Jordan pivot, Gauss?Siedel methods, Horner’s method,
Newton’s method. Methods for solving the area under the normal curve,
Simpson’s method, trapezoidal method. (PR BC 12, Math 35)

Math 56 Introduction to Topology (3 units)

Sets and relations, functions, cardinality, order, topology of the line and plane, topological spaces, bases and subbases, continuity and topological equivalence, metric and normed spaces, countability, separation axioms, compactness, product spaces, connectedness, complete metric spaces, function spaces. (PR Math 38)

Math 58 Mathematical Statistics (3 units)

Distribution of Random Variables, Conditional Probability and Stochastic Dependence, Special Distributions, Distributions of Functions of Random Variables, Limiting Distributions, Estimations and Statistical Hypotheses, Nonparametric Methods, Sufficient statistics, Normal Distribution Theory. (PR Math 16, Math 35)

Math 62 Number Theory (3 units)

Divisibility, Diophantine, Equations, Prime Numbers, Congruences, Multiplicative functions, Solutions to equations involving congruences, sums of squares, primitive roots, Quadratic reciprocity. (PR Math 35)

Math 67 Math Research I (3 units)

Production of research based on most recent developments in mathematics as published in math journals. All research titles must be with the approval of the research adviser and department chairman. (4th Year Level)

Math 68 Math Research II (3 units)

Mathematics research paper writing: elements of math research paper, formulation of abstract, objectives, results, and other parts of a formal research output. (PR Math 67)