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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:
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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           * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified.
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i. Quadratic Forms     * 2. Calculus
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ii. Group theory           * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
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iii. Abstract algebra           * 2.2. 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 I [[attachment:number_theory.primes_0.5.sws]]
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c. Sage math functions (sage as calculator), sage constants           * 5.2. Elementary Number Theory II [Erik]
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d. Generate Classroom examples           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
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i. show (), latex()           * 5.7. Quaternion Algebra [Sourav]
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ii. matplotlab     * 9. About this document ...
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3) Demonstrate SAGE functionality:
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a. Primes
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b. Random numbers == To Do ==
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c. Plotting     * 1. Basics
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d. Interact           * 1.3. Programming in Sage
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e. Sage data types           * 1.5. 2D and 3D Plotting in Sage
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f. Email(?)           * 1.6. Interact in Sage [Erik]
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4) Programming     * 2. Calculus
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a. Types, casting, relevant Sage data types           * 2.3. Multivariate Calculus
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b. Lists, tuples           * 2.4. Taylor Series and Infinite Sums
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c. Control operators (if, then, else, logical operators, in, srange())           * 2.5. Differential Equations
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d. Loops     * 3. Linear Algebra
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i. For, in, srange(), range()           * 3.2. Vector Spaces [Sourav]
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e. Functions     * 4. Abstract Algebra
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f. Recursion           * 4.2. Rings and Fields [Erik]
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5) Topics     * 5. Number Theory
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a. Primes and factorization           * 5.3. Cryptography [Dan]
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i. Given a random number, is it a prime?           * 5.4. Elliptic Curves [Aly]
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1. Modular division           * 5.6. Automorphic Forms
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a. random()           * 5.8. Modular Forms
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b. Factor()     * 6. Combinatorics
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2. Euclidean algorithm           * 6.1. Counting
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a. Recursion           * 6.2. Graph Theory
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b. gcd()     * 7. Geometry
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3. primality testing     * 8. Statistics
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a. for loops           * 8.1. Statistical Methods [Erik]
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b. range()           * 8.2. Probability [Erik]
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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

  1. Sage Primers
    1. Done / In Progress
    2. To Do

Done / In Progress

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

days13/projects/sagenewbie (last edited 2011-01-28 07:12:10 by Eviatar)