Listed in: Mathematics and Statistics, as MATH-382
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Gabriel E. Sosa Castillo (Section 01)
The study of geometric objects by means of their defining equations dates back to the introduction of coordinates by Descartes in 1637. The advent of computers, along with the increase in their processing speed in the last sixty years, has revolutionized the subject, shaping the fields of computational commutative algebra and computational algebraic geometry.
This course will start by studying the theory of Gröbner bases, introduced in 1965, which make possible the implementation of algorithms that facilitate the manipulation and understanding of algebraic equations. We will also develop a dictionary between algebra and geometry, exploring the structure of ideals in polynomial rings and their quotients. In addition, we will discuss the significance of monomial and binomial ideals. The course will end with student presentations on applications of algebraic geometry to robotics, invariant theory, graph theory, algebraic statistics, and other topics. Four class hours per week, including a weekly one-hour computer lab.
Requisite: MATH 350 or consent of the instructor. Spring semester. Professor Sosa Castillo.
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