Courses
MATH 100
Tools for quantitative reasoning and basic college level mathematical concepts for social science students. Mathematics of finance, linear equations and matrices, probability, game theory, derivative, integral, special functions: log, exp, trigonometric and function sketching techniques.
MATH 103
Sets; logic and implications; proof techniques with examples; mathematical induction and well-ordering; equivalence relations; functions; cardinality; countable and uncountable sets.
MATH 107
Vectors; matrices and systems of linear equations; vector spaces; linear maps; orthogonality; algebra of complex numbers; eigenvalue problems.
MATH 203
Functions of several variables; partial differentiation; directional derivatives; exact differentials; multiple integrals and their applications; vector analysis; line and surface integrals; Green?s, Divergence and Stoke?s theorems.
MATH 206
Natural numbers; modular arithmetic; introduction to groups; cyclic and permutation groups; homomorphisms and isomorphisms; normal; factor, simple and free groups; introduction to rings, integral domains, and fields; factor rings and ideals; extension fields; outline of Galois theory.
MATH 102
Limit of a function; Continuous functions and their properties; Derivative andapplications; Extreme values; Indefinite integral; Riemann integral and fundamental theorem of calculus; Logarithmic and exponential functions; L?Hospital?s rule; Sequence and series of numbers; Power series and their properties;
MATH 106
Limits and continuity; derivative and properties of differentiable functions; mean value theorems, Taylor's formula, extreme values; indefinite integral and integral rules; Riemann integral and fundamental theorem of calculus; L'Hospital's rule; improper integrals.
MATH 202
A course in basic concepts and tools of statistics for students who will study social and Behavioral sciences. Topics to be covered are representation of quantitative information in social sciences, forms of numerical data, creating and interpreting graphical and tabular summaries of data, descriptive statistics, estimation of population parameters, confidence intervals, basic hypothesis testing, t-statistics, chi-squared tests and analysis of variance.
MATH 205
Natural numbers; modular arithmetic; introduction to groups; cyclic and permutation groups; homomorphisms and isomorphisms; normal; factor, simple and free groups; introduction to rings, integral domains, and fields; factor rings and ideals; extension fields; outline of Galois theory.
MATH 208
Completeness axiom for real numbers; convergent sequences; compactness; continuous functions; differentiation; linear and topological structure of Euclidean spaces; limit, compactness and connectedness in a Euclidean space; continuity and differentiation of functions of several variables; inverse and implicit function theorems.
MATH 101
Linear algebra and matrix theory; mathematics of finance; counting and the fundamentals of probability theory; game theory.
MATH 104
Counting problems; combinatorial methods; integers, divisibility and primes; graphs and trees; combinatorics in geometry; introduction to complexity and cryptography.
MATH 201
Descriptive statistics; measures of association, correlation, simple regression; probability theory, conditional probability, independence; random variables and probability distributions; sampling distributions; estimation; inference (confidence intervals and hypothesis testing). Topics are supported by computer applications.
MATH 204
First order differential equations. Second order linear equations. Series solutions of ODE?s. The Laplace transform and applications. Systems of first order linear equations. Nonlinear equations and systems:existence, uniqueness and stability of solutions. Fourier series and partial differential equations.
MATH 207
Review of Unique Factorization Domains and Principal IdeaI Domains, Maximal and prime ideals, Nilradical, Local rings, Modules, Cayley-Hamilton theorem, Nakayama's lemma, Exact and split exact sequences, Noetherian rings, Noetherian modules, Hilbert basis theorem, Integral extensions, Integral closure, Non-singularity, Normal rings, Noether normalization, Hilbert nullstellensatz, Spec(A), Localization, Support of a module and the associated primes, Discrete valuation rings, Trace and separability, Completion, Artin-Rees Lemma, An overview of further topics: Dimension theory, Regular rings, Connections with geometric notions.