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MATH M347: Discrete Mathematics
3.00 Credits
Indiana University-South Bend
P: MATH-M 212 or MATH-M 216. Injective and surjective functions; inverse functions; composition; reflexive, symmetric, and transitive relations; equivalence relations; sets including complements, products, and power sets; cardinality; introductory logic including truth tables and quantification; elementary techniques of proof including induction and recursion; counting techniques; graphs and trees; discrete probability. II
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MATH M347 - Discrete Mathematics
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MATH M365: Introduction to Probability And Statistics
3.00 - 4.00 Credits
Indiana University-South Bend
P: MATH-M 209 or MATHM 212, or MATH-M 216. Elementary concepts of probability and statistics. Combinatorics, conditional probability, independence, random variables, moments, Chebyshev inequality, law of large numbers, discrete and continuous distributions. Statistical inference, point and interval estimation, tests of hypotheses. Applications to social, behavioral, and natural sciences. Credit not given for MATH-M 365 and MATH-M 463/MATH-M 466. I (even years)
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MATH M365 - Introduction to Probability And Statistics
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MATH M380: History of Mathematics
3.00 Credits
Indiana University-South Bend
P: MATH-M 208, MATH-M 211, or MATH-M 215. The development of mathematics with emphasis on the modern period; role of proof and truth; discovery of non-Euclidian geometry; rigorization of calculus; the rise of algebra; the paradoxes of set theory; logicist, formalist, and intuitionist responses. I (odd years)
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MATH M380 - History of Mathematics
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MATH M403: Introduction to Modern Algebra I
3.00 Credits
Indiana University-South Bend
P: MATH-M 301and MATH-M 347. Study of groups, rings, and fields, including subgroups, normal subgroups, factor groups, homomorphisms, isomorphisms, finite abelian groups, and beginning the study of rings; including subrings, ideals, and polynomial rings. In those years when MATH-M 405 is taught rather than MATH-M 404, some topics may be omitted and replaced by others from MATH-M 404 to provide a survey course in modern algebra. I (even years)
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MATH M403 - Introduction to Modern Algebra I
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MATH M404: Introduction to Modern Algebra II
3.00 Credits
Indiana University-South Bend
P: MATH-M 403 or consent of instructor. Study of groups, rings, and fields. II (not regularly scheduled)
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MATH M404 - Introduction to Modern Algebra II
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MATH M405: Number Theory
3.00 Credits
Indiana University-South Bend
P: MATH-M 212 or MATH-M 216. Numbers and their representation, divisibility and factorization, primes and their distribution, number theoretic functions, congruences, primitive roots, diophantine equations, quadratic residues, sums of squares, number theory and analysis, algebraic numbers, irrational and transcendental numbers, coding theory, cryptography, or other selected applications. II (not regularly scheduled)
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MATH M405 - Number Theory
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MATH M409: Linear Transformations
3.00 Credits
Indiana University-South Bend
P: MATH-M 301. The study of linear transformations on a finite dimensional vector space over the complex field. Canonical forms, similarity theory; inner products, dual spaces, and diagonalization of normal transformations. P = Prerequisite, R = Recommended, C = Concomitant I = fall semester, II = spring semester, S = summer session(s)
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MATH M409 - Linear Transformations
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MATH M413: Introduction to Analysis I
3.00 Credits
Indiana University-South Bend
P: MATH-M 347 or three courses at or above the 300- level. It is strongly recommended that students who have had little experience writing proofs take MATH-M 347 before taking MATH-M 413. The real numbers, topology of Cartesian spaces, continuity, derivatives, sequences and series of functions, the Riemann-Stieltjes integral. I (not regularly scheduled)
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MATH M413 - Introduction to Analysis I
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MATH M414: Introduction to Analysis II
3.00 Credits
Indiana University-South Bend
P: MATH-M 413. The real numbers, topology of Cartesian spaces, continuity, derivatives, sequences and series of functions, the Riemann-Stieltjes integral. II (not regularly scheduled)
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MATH M414 - Introduction to Analysis II
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MATH M415: Elementary Complex Variables With Applications
3.00 Credits
Indiana University-South Bend
P: MATH-M 311. Algebra and geometry of complex numbers, elementary functions of a complex variable, power series, integration, calculus of residues, conformal mappings and applications. II (not regularly scheduled)
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MATH M415 - Elementary Complex Variables With Applications
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