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| Major Goals: | = Sage Primers = |
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| 1. SAGE as a Smart Calculator (from the students' point of view) 2. SAGE Primers |
<<TableOfContents>> |
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| LINKS: | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
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| http://docutils.sourceforge.net/rst.html | == Done / In Progress == |
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| Sage Tutorial | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
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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]] |
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| 2) Anticipated user desires | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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| a. Content specific modules | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
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| i. Quadratic Forms | * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman |
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| ii. Group theory | * 1.5. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified., [[attachment: development_for_newbies.sws]] |
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| iii. Abstract algebra | * 2. Calculus |
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| iv. Calculus | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
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| v. Number theory | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
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| vi. High school algebra / trigonometry / precalculus | * 2.3. Integral Calculus [Sourav] |
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| vii. Probability | * 3. Linear Algebra |
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| viii. Statistics | * 3.1. Matrix Algebra [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 | * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
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| d. Generate Classroom examples | * 5. Number Theory |
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| i. show (), latex() | * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] |
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| ii. matplotlab | * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] |
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| 3) Demonstrate SAGE functionality: | * 5.7. Quaternion Algebra [Sourav] |
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| a. Primes | * 9. About this document ... |
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| b. Random numbers | |
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| c. Plotting | |
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| d. Interact | == To Do == |
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| e. Sage data types | * 1. Basics |
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| f. Email(?) | * 1.3. Programming in Sage |
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| 4) Programming | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
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| a. Types, casting, relevant Sage data types | * 1.6. Interact in Sage [Erik] |
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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() | * 8.3. Finance |
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| 2. plotting example | |
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| 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 (?) |
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Sage Primers
Contents
Todo: Polish up these primers and put them in the Sage Constructions document.
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 Ploting_with_Sage_v1.0.1.sws by Jose Guzman
1.4. Solving basic equations with Sage Ball_motion.sws by Jose Guzman
1.5. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
- 2. Calculus
2.1. Limits Calculus Analysis_tutorial_Limits_v1.0.2.sws by Jose Guzman
2.2. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.3. 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 [Erik] number_theory.primes_diophantine_equations.1.0.sws
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