Course Content

For our introduction to symbolic computation, we will use the free and open source software SageMath.

There is no textbook for this course, lecture notes are available. The lecture notes are still a work in progress... To save space, older versions of the notes have been deleted.

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

• L-1 Mon 27 Aug 2018: introduction to SageMath (plain text file)
• L-2 Wed 29 Aug 2018: getting started and getting help (Jupyter notebook)
• L-3 Fri 31 Aug 2018: exact and floating-point numbers (Jupyter notebook)
• L-4 Wed 5 Sep 2018: complex and algebraic numbers (Jupyter notebook)
• L-5 Fri 7 Sep 2018: symbols, variables, and references (Jupyter notebook)
• L-6 Mon 10 Sep 2018: data types and data structure (Jupyter notebook)
• L-7 Wed 12 Sep 2018: evaluation and execution (Jupyter notebook)
• L-8 Fri 14 Sep 2018: input/output formats -- saving data (Jupyter notebook)
• L-9 Mon 17 Sep 2018: code generation with Cython (Jupyter notebook)

Part Two: polynomials and expressions

• L-10 Wed 19 Sep 2018: univariate and multivariate polynomials (Jupyter notebook)
• L-11 Fri 21 Sep 2018: rational functions and conversions (Jupyter notebook)
• L-12 Mon 24 Sep 2018: representations of expressions (Jupyter notebook)
• L-13 Wed 26 Sep 2018: substitution, expansion, factorization (Jupyter notebook)
• L-14 Fri 28 Sep 2018: normalizing expressions (Jupyter notebook)
• L-15 Mon 1 Oct 2018: review questions for the first midterm exam (Jupyter notebook)
  with answers in a Jupyter notebook
• L-16 Wed 3 Oct 2018: first midterm exam on the first 14 lectures with answers

Part Three: calculus

• L-17 Fri 5 Oct 2018: defining mathematical functions (Jupyter notebook)
• L-18 Mon 8 Oct 2018: efficient recursive functions (Jupyter notebook)
• L-19 Wed 10 Oct 2018: working with functions (Jupyter notebook)
• L-20 Fri 12 Oct 2018: symbolic and numeric differentiation (Jupyter notebook)
• L-21 Mon 15 Oct 2018: integration and summation (Jupyter notebook)
• L-22 Wed 17 Oct 2018: series and approximations (Jupyter notebook)
• L-23 Fri 19 Oct 2018: symbolic-numeric computation (Jupyter notebook)

Part Four: plotting and solving equations

• L-24 Mon 22 Oct 2018: two dimensional plots (Jupyter notebook)
• L-25 Wed 24 Oct 2018: three dimensional plots (Jupyter notebook)
• L-26 Fri 26 Oct 2018: animations (Jupyter notebook)
• L-27 Mon 29 Oct 2018: solving equations (Jupyter notebook)
• L-28 Wed 31 Oct 2018: linear algebra (Jupyter notebook)
• L-29 Fri 2 Nov 2018: differential equations (Jupyter notebook)
• L-30 Mon 5 Nov 2018: polyhedra and linear programming (Jupyter notebook)
• L-31 Wed 7 Nov 2018: review of lectures 17 to 30 (Jupyter notebook)
• L-32 Fri 9 Nov 2018: second midterm exam on the lectures 17 to 30 with answers

Part Five: advanced topics

• L-33 Mon 12 Nov 2018: building interactive web pages (Jupyter notebook)
  an interactive web page; based on a template page.
• L-34 Wed 14 Nov 2018: an application of interact (Jupyter notebook)
  an interactive web page
• L-35 Fri 16 Nov 2018: symbolic computing with sympy (Jupyter notebook)
• L-36 Mon 19 Nov 2018: scientific computing with scipy (Jupyter notebook)
• L-37 Wed 21 Nov 2018: computational group theory with GAP (Jupyter notebook)
• L-38 Mon 26 Nov 2018: computational number theory with PARI/GP (Jupyter notebook)
• L-39 Wed 28 Nov 2018: computational algebraic geometry with Singular (Jupyter notebook)
• L-40 Fri 30 Nov 2018: statistical computing with R (Jupyter notebook)

Review

• L-41 Mon 3 Dec 2018: first review problems solved in class (Jupyter notebook)
  answers to the first review (Jupyter notebook)
• L-42 Wed 5 Dec 2018: second review problems solving in class (Jupyter notebook)
  answers to the second review (Jupyter notebook)
• L-43 Fri 7 Dec 2018: third review problems solved in class (Jupyter notebook)
  answers to the third review (Jupyter notebook)