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| Describe days13/projects/sagenewbiew here. LINKS: http://docutils.sourceforge.net/rst.html |
= Sage Primers = |
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| Sage Tutorial | <<TableOfContents>> |
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| Goals: | == Done / In Progress == |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 0. Front Matter |
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| 2) Anticipated user desires | * 1. Basics |
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| a. Content specific modules | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| i. Quadratic Forms | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| ii. Group theory | * 1.3. Sage Devel Basics [Erik, Aly] |
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| iii. Abstract algebra | * 1.4. 2D and 3D Plotting in Sage [Erik] |
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| iv. Calculus | * 1.5. Interact in Sage [Erik] |
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| v. Number theory | * 2. Calculus |
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| vi. High school algebra / trigonometry / precalculus | * 2.1. Differential Calculus [[attachment:differential_calculus.sws]] |
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| vii. Probability | * 2.2. Integral Calculus [Sourav] |
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| viii. Statistics | * 3. Linear Algebra |
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| b. Plotting 2 and 3 dimensions | * 3.1. Matrix Algebra [Sourav] |
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| c. Sage math functions (sage as calculator), sage constants | * 4. Abstract Algebra |
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| d. Generate Classroom examples | * 4.1. Group Theory [[attachment:group_theory.txt]] (by Robert Beezer) |
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| i. show (), latex() | * 5. Number Theory |
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| ii. matplotlab | * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] |
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| 3) Demonstrate SAGE functionality: | * 5.2. Elementary Number Theory II [Erik] |
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| a. Primes | * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] |
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| b. Random numbers | * 5.7. Quaternion Algebra [Sourav] |
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| c. Plotting | * 9. About this document ... |
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| d. Interact | |
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| e. Sage data types | |
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| f. Email(?) | == To Do == |
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| 4) Programming | * 1. Basics |
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| a. Types, casting, relevant Sage data types | * 1.3. Programming in Sage |
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| b. Lists, tuples | * 2. Calculus |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 2.3. Multivariate Calculus |
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| d. Loops | * 2.4. Taylor Series and Infinite Sums |
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| i. For, in, srange(), range() | * 2.5. Differential Equations |
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| e. Functions | * 3. Linear Algebra |
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| f. Recursion | * 3.2. Vector Spaces [Sourav] |
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| 5) Topics | * 4. Abstract Algebra |
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| a. Primes and factorization | * 4.2. Rings and Fields [Erik] |
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| i. Given a random number, is it a prime? | * 5. Number Theory |
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| 1. Modular division | * 5.3. Cryptography [Dan] |
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| a. random() | * 5.4. Elliptic Curves [Aly] |
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| b. Factor() | * 5.6. Automorphic Forms |
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| 2. Euclidean algorithm | * 5.8. Modular Forms |
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| a. Recursion | * 6. Combinatorics |
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| b. gcd() | * 6.1. Counting |
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| 3. primality testing | * 6.2. Graph Theory |
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| a. for loops | * 7. Geometry |
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| b. range() | * 8. Statistics |
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| c. is_prime() | * 8.1. Statistical Methods [Erik] |
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| ii. How many primes are there? | * 8.2. Probability [Erik] |
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| 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