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| Deletions are marked like this. | Additions are marked like this. |
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| = Sage for Newbies = | = Sage Primers = |
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| == Major Goals : Sage Primers == | |
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| === Basics === | == Done / In Progress == |
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| * Primer Guidelines [[attachment:primer_template\example.sws]] | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
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| * Primer Design Principles [[attachment:primer_design_principles.rtf]] | * 1. Basics |
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| * SAGE as a Smart Calculator (target: Freshmen) [[attachment:sage_as_a_smart_calculator.sws]] | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
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| === Calculus === | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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| * Differential Calculus (target: Freshmen) [[attachment:differential_calculus.sws]] | * 1.3. Basic 2D plotting with Sage [[attachment:Plotting_with_Sage.sws]] |
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| * Integral Calculus (target: Freshmen) | * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
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| === Number Theory === | * 2. Calculus |
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| * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] | * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
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| * Number Theory via Diophantine Equations (target: Elementary Number Theory students) | * 2.2. Integral Calculus [Sourav] |
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| * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]] | * 3. Linear Algebra |
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| === Abstract Algebra === | * 3.1. Matrix Algebra [Sourav] |
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| * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]] | * 4. Abstract Algebra * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) * 5. Number Theory * 5.1. Elementary Number Theory I [[attachment:number_theory.primes_0.5.sws]] * 5.2. Elementary Number Theory II [Erik] * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] * 5.7. Quaternion Algebra [Sourav] * 9. About this document ... |
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| == Target == | |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | == To Do == |
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| 2) Anticipated user desires | * 1. Basics |
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| a. Content specific modules | * 1.3. Programming in Sage |
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| i. Quadratic Forms | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
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| ii. Group theory | * 1.6. Interact in Sage [Erik] |
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| iii. Abstract algebra | * 2. Calculus |
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| iv. Calculus | * 2.3. Multivariate Calculus |
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| v. Number theory | * 2.4. Taylor Series and Infinite Sums |
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| vi. High school algebra / trigonometry / precalculus | * 2.5. Differential Equations |
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| vii. Probability | * 3. Linear Algebra |
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| viii. Statistics | * 3.2. Vector Spaces [Sourav] |
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| b. Plotting 2 and 3 dimensions | * 4. Abstract Algebra |
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| c. Sage math functions (sage as calculator), sage constants | * 4.2. Rings and Fields [Erik] |
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| d. Generate Classroom examples | * 5. Number Theory |
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| i. show (), latex() | * 5.3. Cryptography [Dan] |
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| ii. matplotlab | * 5.4. Elliptic Curves [Aly] |
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| 3) Demonstrate SAGE functionality: | * 5.6. Automorphic Forms |
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| a. Primes | * 5.8. Modular Forms |
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| b. Random numbers | * 6. Combinatorics |
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| c. Plotting | * 6.1. Counting |
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| d. Interact | * 6.2. Graph Theory |
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| e. Sage data types | * 7. Geometry |
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| 4) Programming | * 8. Statistics |
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| a. Types, casting, relevant Sage data types | * 8.1. Statistical Methods [Erik] |
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| b. Lists, tuples | * 8.2. Probability [Erik] |
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| c. Control operators (if, then, else, logical operators, in, srange()) d. Loops i. For, in, srange(), range() e. Functions f. Recursion 5) Topics a. Primes and factorization i. Given a random number, is it a prime? 1. Modular division a. random() b. Factor() 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. Sage Primer Design Principles Sage Primer Design Principles.pdf primer_design_principles.rtf
- 1. Basics
1.1. Primer Template: An Example primer_template_example.sws
1.2. Sage as a Smart Calculator basics.smart_calculator_0.5.sws
1.3. Basic 2D plotting with Sage Plotting_with_Sage.sws
1.4. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
- 2. Calculus
2.1. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.2. Integral Calculus [Sourav]
- 3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
- 4. Abstract Algebra
4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
5.1. Elementary Number Theory I number_theory.primes_0.5.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
1.5. 2D and 3D Plotting in Sage [JoseGuzman]
- 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