Course Content

There is no textbook for this course, lecture notes are available in pdf and html format. The lecture notes are still a work in progress... to save space the previous lecture notes are removed.

As a reference, you could take a look at Sage for Undergraduates written by Gregory V. Bard.
Another reference is the Sage for Power Users written by William Stein.

Sage worksheets for the lectures are posted below.

Part One: first steps with Sage

• L-1 Mon 11 Jan 2016: introduction to computer algebra
• L-2 Wed 13 Jan 2016: Sage as a calculator, getting help
• L-3 Fri 15 Jan 2016: exact and floating-point numbers
• L-4 Wed 20 Jan 2016: complex and algebraic numbers
• L-5 Fri 22 Jan 2016: symbols, variables, and references
• L-6 Mon 22 Jan 2016: data types and data structures
• L-7 Wed 24 Jan 2016: evaluation and execution
• L-8 Fri 26 Jan 2016: input/output formats -- saving data
• L-9 Mon 1 Feb 2016: code generation with Cython

Part Two: polynomials and expressions

• L-10 Wed 3 Feb 2016: univariate and multivariate polynomials
• L-11 Fri 5 Feb 2016: rational functions and conversions
• L-12 Mon 8 Feb 2016: representation of expressions
• L-13 Wed 10 Feb 2016: substitution, expansion, and factorization
• L-14 Fri 12 Feb 2016: normalizing expressions
• L-15 Mon 15 Feb 2016: questions for the review of the first 14 lectures with some possible answers
• L-16 Wed 17 Feb 2016: first midterm exam on the first 14 lectures with answers

Part Three: calculus

• L-17 Fri 19 Feb 2016: defining mathematical functions
• L-18 Mon 22 Feb 2016: recursive functions and memoization
• L-19 Wed 24 Feb 2016: working with functions
• L-20 Fri 26 Feb 2016: symbolic and numeric differentiation
• L-21 Mon 29 Feb 2016: integration and summation
• L-22 Wed 2 Mar 2016: series, approximations, and limits
• L-23 Fri 4 Mar 2016: symbolic-numeric computation

Part Four: plotting and solving equations

• L-24 Mon 7 Mar 2016: two dimensional plots
• L-25 Wed 9 Mar 2016: plotting in three dimensions and beyond (SageMathCloud worksheet)
• L-26 Fri 11 Mar 2016: animations
• L-27 Mon 14 Mar 2016: solving equations
• L-28 Wed 16 Mar 2016: linear algebra
• L-29 Fri 18 Mar 2016: differential equations
• L-30 Mon 28 Mar 2016: polyhedra and linear programming
• L-31 Wed 30 Mar 2016: review of lectures 17 to 30
• L-32 Fri 1 Apr 2016: second midterm exam on the lectures 17 to 32 with answers

Part Five: advanced Sage

• L-33 Mon 4 Apr 2016: building interactive web pages with corresponding interactive web page.
• L-34 Wed 6 Apr 2016: an application of interact with corresponding Chebyshev four bar mechanism.
• L-35 Fri 8 Apr 2016: symbolic computation with sympy
• L-36 Mon 11 Apr 2016: numeric computation with numpy and scipy
• L-37 Wed 13 Apr 2016: Maxima, a component in Sage
• L-38 Fri 15 Apr 2016: computational group theory with GAP
• L-39 Mon 18 Apr 2016: higher arithmetic with Pari/GP
• L-40 Wed 20 Apr 2016: computing with polynomials in Singular
• L-41 Fri 22 Apr 2016: statistical computing with R

Review

• L-42 Mon 25 Apr 2016: review problems for the first two parts of the course
  with answers in the worksheet
• L-43 Wed 27 Apr 2016: review problems for the materials between the midterms
  with answers in the worksheet
• L-44 Fri 29 Apr 2016: review problems for part five of the course
  with answers in the worksheet