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MA 211: Calculus III
3.00 Credits
Saint Michael's College
Continuation of Mathematics 109-111. Vectors and vector-valued functions, partial differentiation, multiple integrals and their applications, line integrals, Green's Theorem, Stokes' Theorem.Prerequisites: MA 111. Credits: 4 cr.
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MA 211 - Calculus III
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MA 213: Linear Algebra
3.00 Credits
Saint Michael's College
Systems of linear equations; vector spaces; linear independence and bases; direct sums; linear maps; matrices; determinants; eigenvalues and eigenvectors; canonical forms. Prerequisites: MA 211. Credits: 4 cr.
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MA 213 - Linear Algebra
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MA 214: Number Theory
3.00 Credits
Saint Michael's College
Divisibility and prime numbers; congruences and arithmetic modulo n; the Chinese Remainder Theorem; quadratic residues; Diophantine equations. Credits: 3 cr.
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MA 214 - Number Theory
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MA 216: Combinatorics
3.00 Credits
Saint Michael's College
Selected topics from graph theory and enumeration such as isomorphism; planarity; circuits and coloring; search trees and network algorithms. Principles of counting; induction; permutations, combinations, and the binomial theorem; inclusion and exclusion principles; pigeonhole principle; partitions. Additional topics may be chosen from Stirling numbers, generating functions, graph theory, designs, partially ordered sets, codes. Credits: 3 cr.
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MA 216 - Combinatorics
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MA 251: Probability and Statistics
3.00 Credits
Saint Michael's College
Introduction to combinatorics and probability; discrete distributions; density functions, moments; the normal and exponential distributions with applications; the Central Limit Theorem. Elementary applications to Statistics. Prerequisites: MA 111 Credits: 4 cr.
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MA 251 - Probability and Statistics
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MA 303: Differential Equations
3.00 Credits
Saint Michael's College
First order differential equations with applications including examples from biology and physics; qualitative analysis; approximation of solutions. Second order linear equations and applications; series solutions, systems of differential equations. Other topics may include phase plane analysis, Laplace transforms, boundary value problems, difference equations. Prerequisites: MA 211 Credits: 4 cr.
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MA 303 - Differential Equations
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MA 304: History of Mathematics
3.00 Credits
Saint Michael's College
A problem study approach to the history of mathematics emphasizing student participation. Topics may include: number systems, Babylonian and Egyptian mathematics, Pythagorean mathematics, duplication, trisection and quadrature, Greek mathematics including Euclid's Elements, Hindu-Arabian and Chinese mathematics, and the prelude to and dawn of modern mathematics. Prerequisites: MA 111 Credits: 3 cr.
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MA 304 - History of Mathematics
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MA 305: Numerical Methods
3.00 Credits
Saint Michael's College
Methods for approximating the solutions to mathematical problems which are difficult or impossible to solve exactly. Topics include floating-point representations; approximation of functions; roots of nonlinear equations; numerical differentiation and integration; interpolation and curve-fitting; systems of linear equations; and numerical solution of ordinary differential equations. Prerequisites: MA 111 Credits: 3 cr.
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MA 305 - Numerical Methods
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MA 308: Euclidean and Non-Euclidean Geometries
3.00 Credits
Saint Michael's College
Among the topics considered are Euclid's geometry, informal logic, Hilbert's axioms, neutral geometry, the history of the parallel postulate, the discovery of non-Euclidean geometry, the independence of the parallel postulate, and some of the philosophical implications of these topics. Especially useful for prospective teachers of mathematics.Prerequisites: MA 111 Credits: 3 cr.
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MA 308 - Euclidean and Non-Euclidean Geometries
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MA 315: Complex Analysis
3.00 Credits
Saint Michael's College
The topology and the algebraic structure of the complex numbers; differentiation and integration of complex-valued functions; power series and Laurent series; Cauchy's theorem and the residue calculus. Prerequisites: MA 211 Credits: 3 cr.
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MA 315 - Complex Analysis
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