Syllabus for Math 480b:
Sage – Open Source Mathematical Software
William Stein
Spring 2009
• Goal: Teach you to solve problems in linear algebra, abstract algebra, combinatorics, probability,
calculus, and number theory using the open source mathematical software Sage.
• Course webpage: http://wiki.wstein.org/09/480b
• Office Hours: Tuesdays 9–11am.
• Grading:
– There will be no exams at all.
– Your grade will be based entirely on homework.
– There will be 9 homework assignments, and your lowest homework grade will be dropped.
– Your course grade will be at least a 3.5 if you get at least 90%, at least a 2.8 if you get at least
80% on homework, at least a 1.8 if you get at least 70%, and at least 0.8 if you get at least 60%.
I may adjust grades up.
• Prerequisites: Calculus, linear algebra, and experience with some computer programming language.
• Topics: We will cover many of the following, depending on how much time we have.
1. Linear algebra: row reduction of matrices, solving systems of linear equations, computing deter-
minants and characteristic polynomials, finding eigenvalues and eigenvectors, subspaces of vector
spaces
2. Algebra: factoring polynomials, symbolically finding roots of polynomials, solving systems of
polynomial equations, drawing cayley graphs of groups
3. Combinatorics, Probability, and Statistics: plotting graphs (vertices and edges), computing in-
variants of graphs (automorphism group, shortest path, etc.), solving sudoku puzzles and rubik’s
cube, counting and enumerating permutations, combinations, etc., generating random numbers
and random walks, computing the mean, variance, standard deviation, and plotting frequency
histograms, predicting missing data (interpolation)
4. Calculus: plotting functions, computing limits and derivatives, finding min and max points of
functions, computing symbolic integrals, computing definite integrals numerically, numerically
finding roots of polynomials, summing infinite series, solving differential equations, parametric
curves (plotting, arc length)
5. Number theory and cryptography: enumerating and counting prime numbers, exchanging secret
messages (Diffie-Hellman and RSA), attacking RSA and Diffie-Hellman, elliptic curve cryptosys-
tems, determining whether an integer is the area of a rational right triangle
1
本文档为【syllabus M480】，请使用软件OFFICE或WPS软件打开。作品中的文字与图均可以修改和编辑，
图片更改请在作品中右键图片并更换，文字修改请直接点击文字进行修改，也可以新增和删除文档中的内容。
该文档来自用户分享，如有侵权行为请发邮件ishare@vip.sina.com联系网站客服，我们会及时删除。
[版权声明] 本站所有资料为用户分享产生，若发现您的权利被侵害，请联系客服邮件isharekefu@iask.cn，我们尽快处理。
本作品所展示的图片、画像、字体、音乐的版权可能需版权方额外授权，请谨慎使用。
网站提供的党政主题相关内容(国旗、国徽、党徽..)目的在于配合国家政策宣传，仅限个人学习分享使用，禁止用于任何广告和商用目的。
浙公网安备 33021202002483