Computational algebra is the practice of using abstract algebraic structures, to solve problems via computation or to develop algorithms to perform computations. You will learn theoretical results in algebra, tools and algorithms arising from these results, and how to apply the results to problems. At the end of the course, students explore topics of interest in small groups.
This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine the themes of Belonging, Civil Rights, Political Districting, and Algorithms.
The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we’ll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.
The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we’ll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.
Number Theory is the study of the properties of the positive integers. Topics include divisibility, congruences, quadratic reciprocity, numerical functions, Diophantine equations, continued fractions, distribution of primes. Applications will include cryptography - the practice of encrypting and decrypting message, and cryptanalysis - the practice of developing secure encryption and decryption protocols and probing them for possible flaws. Students will also explore topics of interest independently.
Woodbridge native and Hamilton College math professor Courtney Gibbons was recently selected as a Science and Technology Policy Fellow serving the U.S. Congress. Read more.
On this episode of My Favorite Theorem, we were delighted to talk with Courtney Gibbons, a mathematician at Hamilton College, about Emmy Noether’s isomorphism theorems. Listen to Episode 73!
This course is designed to examine issues of social, structural, and institutional hierarchies that intersect with mathematics and statistics. This year, the course will examine the themes of Belonging, Civil Rights, Political Districting, and Algorithms.
The word Algebra and its mathematical connotation stem from a 9th century Arabic treatise by al-Kwarizmi. This historical text dealt with finding the roots of a general quadratic polynomial equation, $ax^2+bx+c = 0$ for nonzero $a$, by completing the square, and this is where our journey begins. By the end of the course, we’ll have an understanding of what tools and techniques modern (19th and 20th century) algebra brings to bear on polynomials and their roots.