Course Name |
Long Title |
Min Credits |
Description |
Requisites |
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An introduction to the theory and properties of integers . Topics |
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MTH-304 |
Number Theory |
3 |
include prime numbers , divisibility and factorization , modular arithmetic , the Euclidean algorithm , linear Diophantine equations , congruencies , the Chinese remainder theorem , and applications in |
Take MTH-231 MTH-246 . ( Required ,
Previous ).
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cryptography . |
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MTH-305 |
Sets , Relations and Functions |
3 |
An introduction to the basic techniques of creating mathematical arguments ( proofs ). Application of proof writing techniques and an indepth study of fundamental concepts and principles that are used throughout mathematics : logic , sets , relations , functions , and infinity through topics such as Cartesian product , partitions , equivalence relations , mathematical induction , set indexing , special functions and transfinite numbers . |
Take MTH-231 MTH-246 . ( Required ,
Previous ).
|
MTH-307 Real Analysis I 3
MTH- 4000
Mathematics Seminar - Capstone 3
MTH-401 Abstract Algebra 3
MTH-407 Probability Theory 3
MTH-408 Mathematical Statistics 3
An in-depth analysis of properties of the real number line , higherdimensional Euclidean spaces and general metric spaces . Limits , sequences and series are studied . The basic theory of functions of a real variable is considered , including continuity , derivatives and integrals . Research on topics related to the student ' s study of mathematics or its related fields . Several projects / papers must be developed and presented . Permission of instructor required . A course in abstract mathematics including the integers , groups , normal subgroups , quotient groups , finite abelian groups , rings , integral domains , ideals , quotient rings , fields , homeomorphisms , isomorphism , real and complex numbers , and polynomials . Probability as a basis for statistical theory and inference . Distributions of random variables , conditional probability , Bayes ' rule , statistical independence , mathematical expectation , probability distributions , probability densities and distribution functions of random variables , joint distributions for two or more random variables , and momentgenerating functions . An in-depth study of the mathematical underpinnings of statistics and the analysis of data . Topics include sampling distributions , estimation theory and applications , hypothesis testing theory and applications , maximum likelihood estimators , regression and correlations , analysis of variance , and nonparametric tests .
Take MTH-305 MTH-246 . ( Required , Previous ).
Take MTH-231 MTH-305 . ( Required , Previous ).
Take MTH-234 MTH-245 MTH-246 . ( Required , Previous ).
Take MTH-407 . ( Required , Previous ).