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MATH 2064: Discrete Mathematics I
4.00 Credits
Transylvania University
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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MATH 2074: Discrete Mathematics II
4.00 Credits
Transylvania University
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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MATH 2084: Differential Equations
4.00 Credits
Transylvania University
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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MATH 2084 - Differential Equations
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MATH 2094: Special Topics in Mathematics
4.00 Credits
Transylvania University
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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MATH 2144: Calculus III
4.00 Credits
Transylvania University
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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MATH 2204: Linear Algebra
4.00 Credits
Transylvania University
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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MATH 2204 - Linear Algebra
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MATH 2504: The Mathematician's Toolkit
4.00 Credits
Transylvania University
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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MATH 3014: Modern Geometry
4.00 Credits
Transylvania University
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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MATH 3014 - Modern Geometry
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MATH 3024: Theory of Numbers
4.00 Credits
Transylvania University
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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MATH 3094: Special Topics in Mathematics
4.00 Credits
Transylvania University
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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MATH 3094 - Special Topics in Mathematics
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