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MATH 214: Topics in Philosophical Logic
4.00 Credits
Lehigh University
The course materials are drawn from the many topics and figures in philosophical logic, widely construed, that are not covered by the other logic courses. Examples of such topics are the many systems of non-classical logic, truth theory, the impact of incompleteness and undecidability results on philosophy, and the foundational projects of many philosophers/mathematicians. The topic may also concern the work of a certain important figure in the history of philosophical logic. Prerequisite: Permission of the instructor. (MA)
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MATH 214 - Topics in Philosophical Logic
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MATH 22: Calculus II fall-spring
4.00 Credits
Lehigh University
Applications of integration; techniques of integration; separable differential equations; infinite sequences and series; Taylor's Theorem and other approximations; curves and vectors in the plane. Prerequisite: MATH 21 or MATH 31. (MA)
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MATH 22 - Calculus II fall-spring
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MATH 229: Geometry
3.00 - 4.00 Credits
Lehigh University
Discussion of geometry as an axiomatic system. Euclid's postulates. History of and equivalent versions of Euclid's fifth postulate. Finite projective geometries. Non- Euclidean geometries based upon negation of the fifth postulate: Geometry on the sphere; Hyperbolic and elliptic geometries. Examination of the concepts of "straight", angle, parallel, symmetry and duality in eachof these geometries. Applications of the different geometries will be considered. Prerequisite: Math 205 or Math 242 or consent of instructor. (MA)
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MATH 229 - Geometry
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MATH 23: Calculus III fall-spring
4.00 Credits
Lehigh University
Vectors in space; partial derivatives; Lagrange multipliers; multiple integrals; vector analysis; line integrals; Green's Theorem, Gauss's Theorem. Prerequisite: MATH 22 or MATH 32. (MA)
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MATH 23 - Calculus III fall-spring
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MATH 230: Numerical Methods fall
3.00 Credits
Lehigh University
Representation of numbers and rounding error; numerical solution of equations; quadrature; polynomial and spline interpolation; numerical solution of initial and boundary value problems. Prerequisites: MATH 205 (previously or concurrently) and knowledge of either FORTRAN or PASCAL. (MA)
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MATH 230 - Numerical Methods fall
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MATH 231: Probability and Statistics fallspring
3.00 Credits
Lehigh University
Probability and distribution of random variables; populations and random sampling; chi-square and t distributions; estimation and tests of hypotheses; correlation and regression theory of two variables. Prerequisite: MATH 22 or MATH 32 or MATH 52. (MA)
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MATH 231 - Probability and Statistics fallspring
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MATH 234: Fractal Geometry
3.00 - 4.00 Credits
Lehigh University
Metric spaces and iterated function systems; various types of fractal dimension; Julia and Mandelbrot sets. Other topics such as chaos may be included. Small amount of computer use. Prerequisite: MATH 23 or MATH 33. (MA)
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MATH 234 - Fractal Geometry
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MATH 242: Linear Algebra fall
3.00 - 4.00 Credits
Lehigh University
Thorough treatment of the solution of simultaneous linear equations in n unknowns, including a discussion of the computational complexity of the calculation. Vector spaces, linear dependence, bases, orthogonality, eigenvalues. Applications as time permits. Prerequisite: MATH 23 or 33 or 52. (MA)
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MATH 242 - Linear Algebra fall
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MATH 243: Algebra spring
3.00 - 4.00 Credits
Lehigh University
Introduction to basic concepts of modern algebra: groups, rings, and fields. (MA)
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MATH 243 - Algebra spring
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MATH 251: Combinatorics
3.00 - 4.00 Credits
Lehigh University
Topics selected from enumeration, graphs and networks, Ramsey theory, ordered sets, min-max duality, and designs. Theory will be motivated by applications from operations research and computer science. Prerequisite: MATH 22 or consent of instructor. (MA)
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MATH 251 - Combinatorics
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