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MATH 261: Discrete Structures
3.00 Credits
Lehigh University
Topics in discrete mathematical structures chosen for their applicability to computer science and engineering. Sets, propositions, induction, recursion; combinatorics; binary relations and functions; ordering, lattices and Boolean algebra; graphs and trees; groups and homomorphisms. Prerequisites: MATH 21. (MA)
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MATH 261 - Discrete Structures
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MATH 271: Readings fall-spring
1.00 - 3.00 Credits
Lehigh University
Study of a topic in mathematics under individual supervision. Intended for students with specific interests in areas not covered in the listed courses. Prerequisite: Consent of the department chair. May be repeated for credit. (MA)
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MATH 271 - Readings fall-spring
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MATH 301: Principles of Analysis I fall
3.00 - 4.00 Credits
Lehigh University
Existence of limits, continuity and uniform continuity; Heine-Borel Theorem; existence of extreme values; mean value theorem and applications; conditions for the existence of the Riemann integral; absolute and uniform convergence; emphasis on theoretical material from the calculus of one variable. Prerequisite: MATH 23 or MATH 33. (MA)
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MATH 301 - Principles of Analysis I fall
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MATH 302: Principles of Analysis II spring
3.00 - 4.00 Credits
Lehigh University
Continuation of MATH 301. Functions of several variables; the implicit function theorem, and further topics with applications to analysis and geometry. Prerequisite: MATH 301. (MA)
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MATH 302 - Principles of Analysis II spring
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MATH 303: Mathematical Logic fall
3.00 - 4.00 Credits
Lehigh University
Detailed proofs are given for the basic mathematical results relating the syntax and semantics of first-order logic (predicate logic): the Soundness and Completeness (and Compactness) Theorems, followed by a brief exposition of the celebrated limitative results of G del, Turing, and Church on incompleteness and undecidability. The material is conceptually rigorous and mathematically mature; the necessary background is a certain degree of mathematical sophistication or a basic knowledge of symbolic logic. Prerequisite: Permission of the instructor. (MA)
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MATH 303 - Mathematical Logic fall
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MATH 304: Axiomatic Set Theory fall
3.00 - 4.00 Credits
Lehigh University
A development of set theory from axioms; relations and functions; ordinal and cardinal arithmetic; recursion theorem; axiom of choice; independence questions. Prerequisite: Permission of instructor. (MA)
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MATH 304 - Axiomatic Set Theory fall
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MATH 307: General Topology I fall
3.00 - 4.00 Credits
Lehigh University
An introductory study of topological spaces, including metric spaces, separation and countability axioms, connectedness, compactness, product spaces, quotient spaces, function spaces. Prerequisite: MATH 301. (MA)
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MATH 307 - General Topology I fall
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MATH 309: Theory of Probability fall
3.00 Credits
Lehigh University
Probabilities of events on discrete and continuous sample spaces; random variables and probability distributions; expectations; transformations; simplest kind of law of large numbers and central limit theorem. The theory is applied to problems in physical and biological sciences. Prerequisite: MATH 23 or MATH 33 or MATH 52. (MA)
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MATH 309 - Theory of Probability fall
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MATH 31: Honors Calculus I fall
4.00 Credits
Lehigh University
Same topics as in MATH 21, but taught from a more thorough and rigorous point of view. (MA)
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MATH 31 - Honors Calculus I fall
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MATH 310: Random Processes and Applications spring
3.00 - 4.00 Credits
Lehigh University
Theory and applications of stochastic processes. Limit theorems, introduction to random walks, Markov chains, Poisson processes, birth and death processes, and Brownian motion. Applications to financial mathematics, biology, business and engineering. Prerequisites: MATH 309 or MATH 231.
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MATH 310 - Random Processes and Applications spring
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