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| ------------ Major Goals: |
= Sage Primers = |
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| 1. SAGE as a Smart Calculator (target: Freshmen) 2. SAGE Primers / Tutorials for (a) Quadratic Forms (target: Arizona Winter School Participants) |
<<TableOfContents>> |
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| (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students) | == Done / In Progress == |
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| * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] | |
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| (c) Number Theory via Primes (target: Elementary Number Theory students) | * 1. Basics |
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| * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] | |
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| (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer] | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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| * 1.3. Basic 2D plotting with Sage [[attachment:Plotting_with_Sage.sws]] | |
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| (e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner] | * 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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| * 2. Calculus | |
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| (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] | * 2.1. Differential Calculus [[attachment: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 [[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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| ------------ Typesetting: |
== To Do == |
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| * 1. Basics | |
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| reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html] | * 1.3. Programming in Sage |
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| * 1.5. 2D and 3D Plotting in Sage | |
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| * 1.6. Interact in Sage [Erik] | |
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| * 2. Calculus | |
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| ------------- | * 2.3. Multivariate Calculus |
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| Goals: | * 2.4. Taylor Series and Infinite Sums |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 2.5. Differential Equations |
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| 2) Anticipated user desires | * 3. Linear Algebra |
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| a. Content specific modules | * 3.2. Vector Spaces [Sourav] |
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| i. Quadratic Forms | * 4. Abstract Algebra |
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| ii. Group theory | * 4.2. Rings and Fields [Erik] |
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| iii. Abstract algebra | * 5. Number Theory |
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| iv. Calculus | * 5.3. Cryptography [Dan] |
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| v. Number theory | * 5.4. Elliptic Curves [Aly] |
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| vi. High school algebra / trigonometry / precalculus | * 5.6. Automorphic Forms |
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| vii. Probability | * 5.8. Modular Forms |
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| viii. Statistics | * 6. Combinatorics |
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| b. Plotting 2 and 3 dimensions | * 6.1. Counting |
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| c. Sage math functions (sage as calculator), sage constants | * 6.2. Graph Theory |
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| d. Generate Classroom examples | * 7. Geometry |
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| i. show (), latex() | * 8. Statistics |
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| ii. matplotlab | * 8.1. Statistical Methods [Erik] |
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| 3) Demonstrate SAGE functionality: | * 8.2. Probability [Erik] |
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| a. Primes b. Random numbers c. Plotting d. Interact e. Sage data types f. Email(?) 4) Programming a. Types, casting, relevant Sage data types b. Lists, tuples 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
- 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