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MATH 306: Intro to Stochastic Processes
3.00 Credits
Loyola University Chicago
For prerequisites and description, see STAT 306, page XX.
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MATH 306 - Intro to Stochastic Processes
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MATH 309: Numerical Methods
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 212 and 264; COMP 170 This course offers an introduction to topics such as error analysis, interpolation and approximation, and the numerical solution of problems involving differentiation, integration, and ordinary and partial differential equations. Outcome: Students will obtain an understanding of how numerical methods can be used in a variety of areas of mathematics.
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MATH 309 - Numerical Methods
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MATH 313: Abstract Algebra
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 201 and 212 This course provides a rigorous introduction to the study of structures such as groups, rings, and fields; emphasis is on the theory of groups with topics such as subgroups, cyclic groups, Abelian groups, permutation groups, homomorphisms, cosets, and factor groups. Outcome: Students will obtain an understanding of abstract structures that will prepare them for advanced work in mathematics.
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MATH 313 - Abstract Algebra
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MATH 314: Adv Topics Abstract Algebra
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 313 This course studies advanced algebraic systems such as commutative and non-commutative rings, integral domains, fields, and additional selected topics. Outcome: Students will obtain an understanding of advanced abstract structures that will prepare them for graduate level work in mathematics.
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MATH 314 - Adv Topics Abstract Algebra
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MATH 315: Advanced Topics in Linear Algebra
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 313 This course offers a rigorous abstract approach to vector spaces and transformations, including similarity, duality, canonical forms, inner products, bilinear forms, Hermitian and unitary spaces, and other selected topics. Outcome: Students will obtain an understanding of advanced linear algebra structures that will prepare them for graduate level work in mathematics.
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MATH 315 - Advanced Topics in Linear Algebra
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MATH 318: Combinatorics
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 162 This course offers a rigorous introduction to combinatorics, including topics such as induction, the pigeon-hole principle, permutations, combinations, recurrence relations, generating functions, the inclusion-exclusion principle, and other selected topics. Outcome: Students will obtain an understanding of the basic topics in combinatorics that will prepare them for advanced study of related topics in mathematics and computer science.
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MATH 318 - Combinatorics
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MATH 320: Mathematical Logic
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 313 This course in modern mathematical logic begins with a study of propositional logic and leads to the study of first-order predicate logic, including quantifiers, models, syntax, semantics, the completeness and compactness theorems, and other selected topics. Outcome: Students will develop a fuller understanding of mathematical logic and therefore of the underlying theory behind proofs of mathematical assertions.
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MATH 320 - Mathematical Logic
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MATH 328: Algebraic Coding Theory
3.00 Credits
Loyola University Chicago
Codes with algebraic structure for error control are examined. Block codes including Hamming codes and Reed-Muller codes, BCH codes, and other cyclic codes and their implementation are treated. Other topics may include: convolutional codes, effciency considerations, and Shannon's fundamental theorem of information theory.
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MATH 328 - Algebraic Coding Theory
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MATH 331: Cryptography
3.00 Credits
Loyola University Chicago
Prerequisite: COMP 363 or MATH 313 or 322. This course introduces the formal foundations of cryptography and also investigates some well-known standards and protocols, including private and public key cryptosystems, hashing, digital signatures, RSA, DSS, PGP, and related topics. Outcome: Students will gain an understanding of cryptosystems widely used to protect data security on the internet, and be able to apply the ideas in new situations as needed.
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MATH 331 - Cryptography
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MATH 344: Geometry
3.00 Credits
Loyola University Chicago
Prerequisite: MATH 212 This course discusses axiomatic systems which define geometries and includes topics from synthetic and analytic projective geometry. Outcome: Students will obtain an understanding of the many different geometries that are studied by teachers and researchers.
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MATH 344 - Geometry
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