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MATH 3008: History of Mathematics
4.00 Credits
Manhattanville College
A survey of some of the central ideas in the development of mathematics. The historical and mathematical context and content of these ideas will be studied along with the major figures responsible for their development. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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MATH 3031: Advanced Calculus
4.00 Credits
Manhattanville College
Emphasis of this course will be on basic concepts of analysis and techniques of proofs. Prerequisite: Calculus III. Corequisite: Fundamental Concepts of Mathematics. ( Spring)
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MATH 3031 - Advanced Calculus
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MATH 3034: Linear Algebra
4.00 Credits
Manhattanville College
This course will discuss vector spaces, linear independence and linear dependence of vectors, bases, subspaces, linear transformations, and representations of linear transformations using matrices. Other topics include determinants, non-singular linear transformations, change of basis, rank of a matrix, orthogonal linear transformations, characteristic values and vectors of linear transformations, similarity and diagonal matrices, and orthogonal reduction of symmetric matrices. A computer symbolic algebra component is included. Prerequisite: Calculus II. Corequisite: Calculus III. ( Fall)
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MATH 3037: Number Theory
4.00 Credits
Manhattanville College
This course will consider basic properties of the natural numbers. Topics include divisibility, primes, congruences, quadratic residues, Gaussian sums, number-theoretic functions, perfect numbers, distribution of primes, and also irrational, algebraic, and transcendental numbers. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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MATH 3040: Modern Algebra
4.00 Credits
Manhattanville College
Basic concepts and structures of modern algebraic systems. Topics covered include: sets, functions, groups and homomorphisms, rings and ideals, fields and field extensions, Galois theory of the roots of polynomials. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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MATH 3040 - Modern Algebra
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MATH 3041: Introduction to Graph Theory
4.00 Credits
Manhattanville College
This course will discuss paths, cycles and properties of trees, planarity and duality, problems relating to the Four-Color map theorem, diagraphs, traversal theory and network flows. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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MATH 3041 - Introduction to Graph Theory
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MATH 3048: Complex Variables
4.00 Credits
Manhattanville College
This course studies the algebraic properties of complex numbers and the notion of an analytic function. Many examples of analytic functions are discussed. The Cauchy Integral Theorem is proved. The course also covers the Cauchy Integral Formula and its consequences, Taylor and Laurent series expansions and the residue theorem and its consequences. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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MATH 3060: Topology
4.00 Credits
Manhattanville College
An introduction to point set topology. Topics covered include: open sets, closed sets, compact sets in metric spaces and topological spaces. Prerequisite: Fundamental Concepts of Mathematics.
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MATH 3060 - Topology
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MATH 3077: Numerical Analysis
4.00 Credits
Manhattanville College
This course offers a study of some basic algorithms of numerical computation with emphasis on the theoretical foundations of the algorithms and various problems related to the practical implementations of the algorithms. Topics covered include: floating point representation, implications of finite precision and errors due to round off, solutions of equations using fixed point method, Newton's method and secant method, numerical integration and differentiation. Prerequisites: Calculus III and Programming and Multimedia in Java.
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MATH 3097: Mathematical Logic
4.00 Credits
Manhattanville College
This course deals with propositional and predicate calculus, G?del's completeness and incompleteness theorems, and undecidable problems. Prerequisite: Fundamental Concepts of Mathematics. ( Every third year)
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