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| Major Goals: | = Sage Primers = |
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| 1. SAGE as a Smart Calculator (from the students' point of view) 2. SAGE Primers |
<<TableOfContents>> |
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| LINKS: | == Done / In Progress == |
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| http://docutils.sourceforge.net/rst.html | * 0. Front Matter |
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| Sage Tutorial | * 1. Basics |
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| Goals: | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| 2) Anticipated user desires | * 1.3. Sage Devel Basics [Erik, Aly] |
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| a. Content specific modules | * 1.4. 2D and 3D Plotting in Sage [Erik] |
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| i. Quadratic Forms | * 1.5. Interact in Sage [Erik] |
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| ii. Group theory | * 2. Calculus |
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| iii. Abstract algebra | * 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
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| iv. Calculus | * 2.2. Integral Calculus [Sourav] |
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| v. Number theory | * 3. Linear Algebra |
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| vi. High school algebra / trigonometry / precalculus | * 3.1. Matrix Algebra [Sourav] |
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| vii. Probability | * 4. Abstract Algebra |
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| viii. Statistics | * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer) |
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| b. Plotting 2 and 3 dimensions | * 5. Number Theory |
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| c. Sage math functions (sage as calculator), sage constants | * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
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| d. Generate Classroom examples | * 5.2. Elementary Number Theory II [Erik] |
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| i. show (), latex() | * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
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| ii. matplotlab | * 5.7. Quaternion Algebra [Sourav] |
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| 3) Demonstrate SAGE functionality: | * 9. About this document ... |
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| a. Primes | |
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| b. Random numbers | |
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| c. Plotting | == To Do == |
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| d. Interact | * 1. Basics |
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| e. Sage data types | * 1.3. Programming in Sage |
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| f. Email(?) | * 2. Calculus |
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| 4) Programming | * 2.3. Multivariate Calculus |
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| a. Types, casting, relevant Sage data types | * 2.4. Taylor Series and Infinite Sums |
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| b. Lists, tuples | * 2.5. Differential Equations |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 3. Linear Algebra |
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| d. Loops | * 3.2. Vector Spaces [Sourav] |
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| i. For, in, srange(), range() | * 4. Abstract Algebra |
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| e. Functions | * 4.2. Rings and Fields [Erik] |
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| f. Recursion | * 5. Number Theory |
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| 5) Topics | * 5.3. Cryptography [Dan] |
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| a. Primes and factorization | * 5.4. Elliptic Curves [Aly] |
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| i. Given a random number, is it a prime? | * 5.6. Automorphic Forms |
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| 1. Modular division | * 5.8. Modular Forms |
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| a. random() | * 6. Combinatorics |
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| b. Factor() | * 6.1. Counting |
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| 2. Euclidean algorithm | * 6.2. Graph Theory |
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| a. Recursion | * 7. Geometry |
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| b. gcd() | * 8. Statistics |
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| 3. primality testing | * 8.1. Statistical Methods [Erik] |
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| a. for loops | * 8.2. Probability [Erik] |
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| b. range() c. is_prime() ii. How many primes are there? 1. prime_pi() 2. plotting example iii. Where are the primes? 1. Density of primes 2. primes() 3. Arithemtic sequences of primes b. Diophantine equations i. Linear Diophantine equation 1. extended euclidean algorithm 2. recursion vs iteration ii. diagonal quadratic forms; sums of squares (ENT p. 25) 1. Pythagorean triples and generating them 2. Graphing the Pythagorean triples 3. Enumerating all triples using linear intersections 4. Elliptic curves and congruent numbers (chapter 6, stein) iii. Pell’s Equation (?) |
* 8.3. Finance |
Sage Primers
Contents
Done / In Progress
- 0. Front Matter
- 1. Basics
1.1. Primer Template: An Example primer_template\example.sws primer_design_principles.rtf
1.2. Sage as a Smart Calculator sage_as_a_smart_calculator.sws
- 1.3. Sage Devel Basics [Erik, Aly]
- 1.4. 2D and 3D Plotting in Sage [Erik]
- 1.5. Interact in Sage [Erik]
- 2. Calculus
2.1. Differential Calculus differential_calculus.sws
- 2.2. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.txt (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory I number_theory.primes_0.1.sws
- 5.2. Elementary Number Theory II [Erik]
5.5. Quadratic Forms quadratic_forms.sws
- 5.7. Quaternion Algebra [Sourav]
- 9. About this document ...
To Do
- 1. Basics
- 1.3. Programming in Sage
- 2. Calculus
- 2.3. Multivariate Calculus
- 2.4. Taylor Series and Infinite Sums
- 2.5. Differential Equations
- 3. Linear Algebra
- 3.2. Vector Spaces [Sourav]
- 4. Abstract Algebra
- 4.2. Rings and Fields [Erik]
- 5. Number Theory
- 5.3. Cryptography [Dan]
- 5.4. Elliptic Curves [Aly]
- 5.6. Automorphic Forms
- 5.8. Modular Forms
- 6. Combinatorics
- 6.1. Counting
- 6.2. Graph Theory
- 7. Geometry
- 8. Statistics
- 8.1. Statistical Methods [Erik]
- 8.2. Probability [Erik]
- 8.3. Finance