UndergraduateCatalog20-21 | Page 235

Gwynedd Mercy University
AY2020-2021 / Undergraduate Academic Catalog
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 ). Prerequisites : MTH-235 , MTH-245 ( Required , Previous ).
MTH-304 Number Theory ( 3 ) 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 . Prerequisites : MTH-231 , MTH-246 ( Required , Previous ).
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 in-depth 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 . Prerequisites : MTH-231 , MTH-246 ( Required , Previous ).
MTH-307 Real Analysis I ( 3 ) An in-depth analysis of properties of the real number line , higher-dimensional 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 . Prerequisites : MTH-305 ( Required , Previous ).
MTH-4000 Mathematics Seminar - Capstone ( 3 ) Research on topics related to the student ' s study of mathematics or its related fields . Several projects / papers must be developed and presented . Prerequisites : Permission of instructor
MTH-401 Abstract Algebra ( 3 ) 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 . Prerequisites : MTH-231 , MTH-305 ( Required , Previous ).
MTH-407 Probability Theory ( 3 ) 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 moment-generating functions . Prerequisites : MTH-234 , MTH-245 , MTH-246 ( Required , Previous ).
MTH-408 Mathematical Statistics ( 3 ) 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
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