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| Deletions are marked like this. | Additions are marked like this. |
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| Describe days13/projects/sagenewbiew here. | = Sage Primers = |
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| LINKS: | <<TableOfContents>> |
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| http://docutils.sourceforge.net/rst.html | == Done / In Progress == |
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| Sage Tutorial | * 0. Front Matter |
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| Goals: | * 1. Basics |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| 2) Anticipated user desires | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| a. Content specific modules | * 1.3. Sage Devel Basics [Erik, Aly] |
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| i. Quadratic Forms | |
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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 [Erik] |
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| f. Email(?) | * 1.5. 2D and 3D Plotting in Sage [Erik] |
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| 4) Programming | * 1.6. Interact in Sage [Erik] |
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| a. Types, casting, relevant Sage data types | * 2. Calculus |
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| b. Lists, tuples | * 2.3. Multivariate Calculus |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 2.4. Taylor Series and Infinite Sums |
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| d. Loops | * 2.5. Differential Equations |
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| i. For, in, srange(), range() | * 3. Linear Algebra |
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| e. Functions | * 3.2. Vector Spaces [Sourav] |
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| f. Recursion | * 4. Abstract Algebra |
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| 5) Topics | * 4.2. Rings and Fields [Erik] |
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| a. Primes and factorization | * 5. Number Theory |
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| i. Given a random number, is it a prime? | * 5.3. Cryptography [Dan] |
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| 1. Modular division | * 5.4. Elliptic Curves [Aly] |
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| a. random() | * 5.6. Automorphic Forms |
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| b. Factor() | * 5.8. Modular Forms |
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| 2. Euclidean algorithm | * 6. Combinatorics |
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| a. Recursion | * 6.1. Counting |
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| b. gcd() | * 6.2. Graph Theory |
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| 3. primality testing | * 7. Geometry |
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| a. for loops | * 8. Statistics |
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| b. range() | * 8.1. Statistical Methods [Erik] |
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| c. is_prime() | * 8.2. Probability [Erik] |
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| 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]
- 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 [Erik]
- 1.5. 2D and 3D Plotting in Sage [Erik]
- 1.6. Interact in Sage [Erik]
- 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