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← Revision 64 as of 2011-01-28 07:12:10 ⇥
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| ## page was renamed from days13/projects/sagenewbiew Major Goals: |
= Sage Primers = |
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| 1. SAGE as a Smart Calculator (from the students' point of view) | <<TableOfContents>> |
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| 2. SAGE Primers for | '''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document. |
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| (a) Quadratic Forms | == Done / In Progress == |
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| (b) | * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]] |
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| LINKS: | * 1. Basics |
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| http://docutils.sourceforge.net/rst.html | * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] |
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| Sage Tutorial | * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]] |
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| Goals: | * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman |
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| 1) Accessible to high school math teachers and undergraduate mathematics majors. | * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman |
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| 2) Anticipated user desires | * 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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| a. Content specific modules | * 2. Calculus |
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| i. Quadratic Forms | * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman |
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| ii. Group theory | * 2.2. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]] |
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| iii. Abstract algebra | * 2.3. Integral Calculus [Sourav] |
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| iv. Calculus | * 3. Linear Algebra |
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| v. Number theory | * 3.1. Matrix Algebra [Sourav] |
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| vi. High school algebra / trigonometry / precalculus | * 4. Abstract Algebra |
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| vii. Probability | * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) |
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| viii. Statistics | * 5. Number Theory |
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| b. Plotting 2 and 3 dimensions | * 5.1. Elementary Number Theory [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]] |
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| c. Sage math functions (sage as calculator), sage constants | * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]] |
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| d. Generate Classroom examples | * 5.7. Quaternion Algebra [Sourav] |
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| i. show (), latex() | * 9. About this document ... |
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| ii. matplotlab | |
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| 3) Demonstrate SAGE functionality: | |
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| a. Primes | == To Do == |
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| b. Random numbers | * 1. Basics |
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| c. Plotting | * 1.3. Programming in Sage |
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| d. Interact | * 1.5. 2D and 3D Plotting in Sage [JoseGuzman] |
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| e. Sage data types | * 1.6. Interact in Sage [Erik] |
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| f. Email(?) | * 2. Calculus |
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| 4) Programming | * 2.3. Multivariate Calculus |
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| a. Types, casting, relevant Sage data types | * 2.4. Taylor Series and Infinite Sums |
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| b. Lists, tuples | * 2.5. Differential Equations |
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| c. Control operators (if, then, else, logical operators, in, srange()) | * 3. Linear Algebra |
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| d. Loops | * 3.2. Vector Spaces [Sourav] |
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| i. For, in, srange(), range() | * 4. Abstract Algebra |
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| e. Functions | * 4.2. Rings and Fields [Erik] |
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| f. Recursion | * 5. Number Theory |
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| 5) Topics | * 5.3. Cryptography [Dan] |
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| a. Primes and factorization | * 5.4. Elliptic Curves [Aly] |
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| i. Given a random number, is it a prime? | * 5.6. Automorphic Forms |
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| 1. Modular division | * 5.8. Modular Forms |
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| a. random() | * 6. Combinatorics |
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| b. Factor() | * 6.1. Counting |
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| 2. Euclidean algorithm | * 6.2. Graph Theory |
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| a. Recursion | * 7. Geometry |
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| b. gcd() | * 8. Statistics |
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| 3. primality testing | * 8.1. Statistical Methods [Erik] |
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| a. for loops | * 8.2. Probability [Erik] |
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| 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
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