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MA 540: Analysis I
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Metric spaces, compactness and connectedness, sequences and series, continuity and uniform continuity, differentiability, Taylor's Theorem, Riemann-Stieltjes integrals.
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MA 540 - Analysis I
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MA 541: Analysis II
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Sequences and series of functions, uniform convergence, equicontinuous families, the Stone-Weierstrass Theorem, Fourier series, introduction to Lebesgue measure and integration.
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MA 541 - Analysis II
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MA 553: Introduction to Abstract Algebra
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Group theory: Sylow theorems, Jordan-Holder theorem, solvable groups. Ring theory: unique factorization in polynomial rings, and principal ideal domains. Field theory: straightedge and compass constructions, roots of unity, finite fields, Galois theory, and solubility of equations by radicals.
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MA 553 - Introduction to Abstract Algebra
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MA 554: Linear Algebra
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Review of basics: vector spaces, dimension, linear maps, matrices, determinants, linear equations. Bilinear forms; inner product spaces; spectral theory; eigenvalues. Modules over a principal ideal domain; finitely generated abelian groups; Jordan and rational canonical forms for a linear transformation.
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MA 554 - Linear Algebra
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MA 556: Introduction to the Theory of Numbers
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Divisibility, congruences, quadratic residues, Diophantine equations, the sequence of primes.
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MA 556 - Introduction to the Theory of Numbers
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MA 560: Fundamental Concepts of Geometry
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Foundations of Euclidean geometry, including a critique of Euclid's Elements and a detailed study of an axiom system such as that of Hilbert. Independence of the parallel axiom and introduction to non-Euclidean geometry.
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MA 560 - Fundamental Concepts of Geometry
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MA 571: Elementary Topology
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Fundamentals of point-set topology with a brief introduction to the fundamental group and related topics; topological and metric spaces; compactness and connectedness; separation properties; local compactness; introduction to function spaces; basic notions involving deformations of continuous paths.
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MA 571 - Elementary Topology
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MA 575: Graph Theory
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Introduction to graph theory with applications.
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MA 575 - Graph Theory
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MA 580: History of Mathematics
3.00 Credits
Indiana University-Purdue University-Fort Wayne
The origins of mathematical ideas and their evolution over time, from early number systems and the evolution of algebra, geometry, and calculus to 20th-century results in the foundations of mathematics. Connections between mathematics and society, including the role of applications in the development of mathematical concepts.
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MA 580 - History of Mathematics
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MA 581: Introduction to Logic for Teachers
3.00 Credits
Indiana University-Purdue University-Fort Wayne
Sentential and general theory of inference and nature of proof, elementary axiom systems.
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MA 581 - Introduction to Logic for Teachers
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