Course Name |
Long Title |
Min Credits |
Description |
Requisites |
MTH-302 |
Differential Equations |
3 |
An introduction to ordinary differential equations and their use in modeling continuous change in the real-world . Topics include both analytical and graphical methods of solving DEs , systems of ordinary differential equations , and important applications like exponential / logistic growth , harmonic oscillators , and predator / prey systems . |
Take MTH-235 MTH-246 . ( Required ,
Previous ).
|
MTH-303 College Geometry and Related Topics 3
MTH-304 Number Theory 3
MTH-305 Sets , Relations and Functions 3
A study of geometry , including euclidean and non-euclidean geometries , axiomatic systems , transformations and isometries , and symmetry . There is a focus on exploration , conjecture , and basic geometric arguments ( proofs ). An introduction to the theory and properties of integers . Topics include prime numbers , divisibility and factorization , modular arithmetic , the Euclidean algorithm , linear Diophantine equations , congruencies , the Chinese remainder theorem , and applications in cryptography . 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-235 MTH-245 . ( Required , Previous ).
Take MTH-231 MTH-246 . ( Required , Previous ).
Take MTH-231 MTH-246 . ( Required , Previous ).
MTH-307 Real Analysis I 3
MTH-4000 Mathematics Seminar - Capstone 3
MTH-401 Abstract Algebra 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 .
Take MTH-305 MTH-246 . ( Required , Previous ).
Take MTH-231 MTH-305 . ( Required , Previous ).