APM 4777/5777: Computer Algebra
384 MSC (Notice the room change)
MW 7:30-9:17 PM
This is a course that is cross-listed as an undergraduate course (APM 4777) and graduate course (APM 5777). Even though the course is taught together the exams and the grading will be very different.
APM 4777 Midterm I: 30 %
Midterm II: 30 %
Final 40 %
The mathematics and algorithms for symbolic computation. Includes theory of algebraic extensions, modular and p-adic methods, Groebner bases, factorization and zeros of polynomials, solutions to systems of polynomial equations, applications to automatic geometric theorem proving and closed form solutions to differential equations.
MTH 2775 with a grade of (C) or higher and knowledge of a scientific computer programming language, or permission of instructor.
A study of the mathematics and algorithms which are used in symbolic algebraic manipulation packages. Topics include computer representation of symbolic mathematics, polynomial ring theory, field theory and algebraic extensions, modular and p-adic methods, subresultant algorithm for polynomial GCD’s, Groebner bases for polynomial ideals and Buchberger’s algorithm, factorization and zeros of polynomials. Required background includes a course in abstract algebra and knowledge of a scientific programming language.
Required background includes a course in abstract algebra.
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra (Undergraduate Texts in Mathematics) 4th ed. 2015 Edition, David A. Cox, John Little, Donald O'Shea
Homework will be assigned and occasionally will be collected to be graded. The following chart will be used to determine your grade:
Grades will be determined with the following scale:
The course will be conducted in accordance to the Oakland University regulations and policies. Details can be found here
Software that will be used
- Addition formulas on Picard curves