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Course Criteria
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4.00 Credits
A survey of mathematical topics that do not involve calculus, with an emphasis on proof techniques. Major topics will include formal logic, number theory, mathematical induction, set theory, and principles of counting. Students will acquire an understanding of the theories involved, as well as computational facility with the topics. Prerequisite: A grade of C- or better in MATH 1304 or permission of the instructor. IV
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4.00 Credits
A continuation of MATH 2064. Major topics will include functions, recurrence relations, set relations, graph theory, and trees. A number of new proof techniques will be introduced. The student will gain an enlarged understanding of the concepts underlying discrete mathematics. Prerequisite: A grade of C- or better in MATH 2064. IV
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4.00 Credits
Standard methods of solving ordinary differential equations, singular solutions, simultaneous differential equations, special second-order differential equations, and applications to geometry, mechanics, and physics. Prerequisite: MATH 1324. IV
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4.00 Credits
Current topics in any field of mathematics atthe sophomore level may be offered when there is demand. May be taken for credit more than once. Prerequisites: Determined by topic. May not be chosen as a major or minor pattern elective in mathematics. IV
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4.00 Credits
A continuation of MATH 1324. Topics on infinite series, vectors in the plane and in threedimensional space, calculus of functions of several variables, partial derivatives, and multiple integration. Prerequisite: A grade of C- or better in MATH 1324. IV
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4.00 Credits
Systems of linear equations and their solution, theory of matrices, linear transformations, characteristic values, and inner product spaces. Prerequisite: Permission of instructor. IV
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4.00 Credits
What do mathematicians do? How is mathematics done? This course explores these questions via an introduction to the mathematical habits of mind and abstract reasoning requisite for the study of mathematics. Core mathematical concepts such as sets, elementary logic, proof techniques, functions and relations, cardinality and counting are studied. Serving as a transition course, the content and philosophy of the course are designed to introduce students to the type of mathematics encountered in upper-level courses. Prerequisite: Math 1324 or permission of instructor. Math majors are strongly encouraged to take this course during their first two years. IV
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4.00 Credits
A survey of modern geometry using both synthetic and analytic points of view. Topics include axiomatics, finite geometries, Euclidean geometry, non-Euclidean geometry, transformational geometry, and geometric constructions. Prerequisite: Permission of instructor. IV
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4.00 Credits
Integers, unique factorization, linear Diophantine equations, congruences, Fermat's and Wilson's theorems, divisors, perfect numbers, Euler's theorem and function, primitive roots and indices, quadratic congruences, numbers in other bases, Pythagorean triangles, and sums of two squares. Prerequisite: Permission of instructor. IV
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4.00 Credits
Topics such as topology, differential geometry, complex variables, advanced differential equations, and operations research are offered when there is demand. May be taken for credit more than once. Prerequisite: Determined by topic. May be chosen as a major pattern elective in mathematics or teaching mathematics. IV
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