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Describe days13/projects/sagenewbiew here. = Sage Primers =
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Sage Tutorial <<TableOfContents>>
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Goals:
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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_0.4.sws]]
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iii. Abstract algebra           * 1.4. Sage Devel Basics [Erik, Aly]
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iv. Calculus     * 2. Calculus
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v. Number theory           * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]
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vi. High school algebra / trigonometry / precalculus           * 2.2. 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 I [[attachment:number_theory.primes_0.5.sws]]
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ii. matplotlab           * 5.2. Elementary Number Theory II [Erik]
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3) Demonstrate SAGE functionality:           * 5.5. Quadratic Forms [[attachment:quadratic_forms.sws]]
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a. Primes           * 5.7. Quaternion Algebra [Sourav]
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b. Random numbers     * 9. About this document ...
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c. Plotting
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d. Interact
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e. Sage data types == To Do ==
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f. Email(?)     * 1. Basics
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4) Programming           * 1.3. Programming in Sage
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a. Types, casting, relevant Sage data types           * 1.5. 2D and 3D Plotting in Sage
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b. Lists, tuples           * 1.6. Interact in Sage [Erik]
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c. Control operators (if, then, else, logical operators, in, srange())     * 2. Calculus
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d. Loops           * 2.3. Multivariate Calculus
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i. For, in, srange(), range()           * 2.4. Taylor Series and Infinite Sums
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e. Functions           * 2.5. Differential Equations
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f. Recursion     * 3. Linear Algebra
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5) Topics           * 3.2. Vector Spaces [Sourav]
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a. Primes and factorization     * 4. Abstract Algebra
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i. Given a random number, is it a prime?           * 4.2. Rings and Fields [Erik]
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1. Modular division     * 5. Number Theory
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a. random()           * 5.3. Cryptography [Dan]
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b. Factor()           * 5.4. Elliptic Curves [Aly]
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2. Euclidean algorithm           * 5.6. Automorphic Forms
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a. Recursion           * 5.8. Modular Forms
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b. gcd()     * 6. Combinatorics
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3. primality testing           * 6.1. Counting
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a. for loops           * 6.2. Graph Theory
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b. range()     * 7. Geometry
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c. is_prime()     * 8. Statistics
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ii. How many primes are there?           * 8.1. Statistical Methods [Erik]
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1. prime_pi()           * 8.2. Probability [Erik]
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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)