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| = Sage for Newbies = | = Sage Primers = |
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| == Major Goals : Sage Primers == | == Done / In Progress == |
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| === Basics === | * 0. Front Matter |
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| * Primer Guidelines [[attachment:primer_template\example.sws]] | * 1. Basics |
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| * Primer Design Principles [[attachment:primer_design_principles.rtf]] | * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] |
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| * SAGE as a Smart Calculator (target: Freshmen) [[attachment:sage_as_a_smart_calculator.sws]] | * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] |
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| === Calculus === * Differential Calculus (target: Freshmen) [[attachment:differential_calculus.sws]] * Integral Calculus (target: Freshmen) === Number Theory === * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] * Number Theory via Diophantine Equations (target: Elementary Number Theory students) * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]] === Abstract Algebra === * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]] |
* 1.3. Sage Devel Basics [Erik, Aly] |
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| == Target == | * 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 [Erik] |
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| a. Primes | * 1.5. 2D and 3D Plotting in Sage [Erik] |
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| b. Random numbers | * 1.6. Interact in Sage [Erik] |
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| c. Plotting | * 2. Calculus |
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| d. Interact | * 2.3. Multivariate Calculus |
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| e. Sage data types | * 2.4. Taylor Series and Infinite Sums |
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| 4) Programming | * 2.5. Differential Equations |
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| a. Types, casting, relevant Sage data types | * 3. Linear Algebra |
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| b. Lists, tuples | * 3.2. Vector Spaces [Sourav] |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 4. Abstract Algebra |
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| d. Loops | * 4.2. Rings and Fields [Erik] |
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| i. For, in, srange(), range() | * 5. Number Theory |
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| e. Functions | * 5.3. Cryptography [Dan] |
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| f. Recursion | * 5.4. Elliptic Curves [Aly] |
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| 5) Topics | * 5.6. Automorphic Forms |
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| a. Primes and factorization | * 5.8. Modular Forms |
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| i. Given a random number, is it a prime? | * 6. Combinatorics |
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| 1. Modular division | * 6.1. Counting |
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| a. random() | * 6.2. Graph Theory |
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| b. Factor() | * 7. Geometry |
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| 2. Euclidean algorithm | * 8. Statistics |
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| a. Recursion | * 8.1. Statistical Methods [Erik] |
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| b. gcd() | * 8.2. Probability [Erik] |
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| 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
- 1.3. 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