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| ## page was renamed from days13/projects/sagenewbiew Major Goals: |
= Sage Primers = |
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| 1. SAGE as a Smart Calculator (from the students' point of view) | <<TableOfContents>> |
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| 2. SAGE Primers for | == Done / In Progress == |
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| (a) Quadratic Forms | * 0. Front Matter |
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| (b) | * 1. Basics |
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| LINKS: | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| http://docutils.sourceforge.net/rst.html | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| Sage Tutorial | * 1.4. Sage Devel Basics [Erik, Aly] |
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| Goals: | * 2. Calculus |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
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| 2) Anticipated user desires | * 2.2. Integral Calculus [Sourav] |
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| a. Content specific modules | * 3. Linear Algebra |
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| i. Quadratic Forms | * 3.1. Matrix Algebra [Sourav] |
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| ii. Group theory | * 4. Abstract Algebra |
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| iii. Abstract algebra | * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer) |
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| iv. Calculus | * 5. Number Theory |
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| v. Number theory | * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
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| vi. High school algebra / trigonometry / precalculus | * 5.2. Elementary Number Theory II [Erik] |
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| vii. Probability | * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
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| viii. Statistics | * 5.7. Quaternion Algebra [Sourav] |
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| b. Plotting 2 and 3 dimensions | * 9. About this document ... |
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| c. Sage math functions (sage as calculator), sage constants | |
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| d. Generate Classroom examples | |
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| i. show (), latex() | == To Do == |
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| ii. matplotlab | * 1. Basics |
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| 3) Demonstrate SAGE functionality: | * 1.3. Programming in Sage |
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| a. Primes | * 2. Calculus |
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| b. Random numbers | * 2.3. Multivariate Calculus |
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| c. Plotting | * 2.4. Taylor Series and Infinite Sums |
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| d. Interact | * 2.5. Differential Equations |
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| e. Sage data types | * 3. Linear Algebra |
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| f. Email(?) | * 3.2. Vector Spaces [Sourav] |
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| 4) Programming | * 4. Abstract Algebra |
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| a. Types, casting, relevant Sage data types | * 4.2. Rings and Fields [Erik] |
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| b. Lists, tuples | * 5. Number Theory |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 5.3. Cryptography [Dan] |
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| d. Loops | * 5.4. Elliptic Curves [Aly] |
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| i. For, in, srange(), range() | * 5.6. Automorphic Forms |
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| e. Functions | * 5.8. Modular Forms |
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| f. Recursion | * 6. Combinatorics |
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| 5) Topics | * 6.1. Counting |
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| a. Primes and factorization | * 6.2. Graph Theory |
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| i. Given a random number, is it a prime? | * 7. Geometry |
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| 1. Modular division | * 8. Statistics |
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| a. random() | * 8.1. Statistical Methods [Erik] |
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| b. Factor() | * 8.2. Probability [Erik] |
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| 2. Euclidean algorithm a. Recursion b. gcd() 3. primality testing a. for loops 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
- 1.4. Sage Devel Basics [Erik, Aly]
- 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