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Describe days13/projects/sagenewbiew here. LINKS: http://docutils.sourceforge.net/rst.html |
= Sage Primers = |
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Sage Tutorial | <<TableOfContents>> |
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Goals: | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
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1) Accessible to high school math teachers and undergraduate mathematics majors. | == Done / In Progress == |
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2) Anticipated user desires | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
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a. Content specific modules | * 1. Basics |
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i. Quadratic Forms | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
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ii. Group theory | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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iii. Abstract algebra | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
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iv. Calculus | * 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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v. Number theory | * 2. Calculus |
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vi. High school algebra / trigonometry / precalculus | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
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vii. Probability | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
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viii. Statistics | * 2.3. Integral Calculus [Sourav] |
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b. Plotting 2 and 3 dimensions | * 3. Linear Algebra |
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c. Sage math functions (sage as calculator), sage constants | * 3.1. Matrix Algebra [Sourav] |
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d. Generate Classroom examples | * 4. Abstract Algebra |
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i. show (), latex() | * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
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ii. matplotlab | * 5. Number Theory |
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3) Demonstrate SAGE functionality: | * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] |
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a. Primes | * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] |
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b. Random numbers | * 5.7. Quaternion Algebra [Sourav] |
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c. Plotting | * 9. About this document ... |
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d. Interact | |
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e. Sage data types | |
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f. Email(?) | == To Do == |
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4) Programming | * 1. Basics |
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a. Types, casting, relevant Sage data types | * 1.3. Programming in Sage |
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b. Lists, tuples | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
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c. Control operators (if, then, else, logical operators, in, srange()) | * 1.6. Interact in Sage [Erik] |
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d. Loops | * 2. Calculus |
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i. For, in, srange(), range() | * 2.3. Multivariate Calculus |
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e. Functions | * 2.4. Taylor Series and Infinite Sums |
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f. Recursion | * 2.5. Differential Equations |
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5) Topics | * 3. Linear Algebra |
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a. Primes and factorization | * 3.2. Vector Spaces [Sourav] |
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i. Given a random number, is it a prime? | * 4. Abstract Algebra |
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1. Modular division | * 4.2. Rings and Fields [Erik] |
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a. random() | * 5. Number Theory |
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b. Factor() | * 5.3. Cryptography [Dan] |
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2. Euclidean algorithm | * 5.4. Elliptic Curves [Aly] |
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a. Recursion | * 5.6. Automorphic Forms |
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b. gcd() | * 5.8. Modular Forms |
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3. primality testing | * 6. Combinatorics |
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a. for loops | * 6.1. Counting |
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b. range() | * 6.2. Graph Theory |
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c. is_prime() | * 7. Geometry |
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ii. How many primes are there? | * 8. Statistics |
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1. prime_pi() | * 8.1. Statistical Methods [Erik] |
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2. plotting example | * 8.2. Probability [Erik] |
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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 (?) |
* 8.3. Finance |
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. 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