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Describe days13/projects/sagenewbiew here. = Sage for Newbies =
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LINKS: <<TableOfContents>>
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http://docutils.sourceforge.net/rst.html == Done ==
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Sage Tutorial     * 0. Front Matter
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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]] [[attachment:primer_design_principles.rtf]]
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2) Anticipated user desires           * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
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a. Content specific modules     * 2. Calculus
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i. Quadratic Forms           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]
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ii. Group theory     * 4. Abstract Algebra
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iii. Abstract algebra           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
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iv. Calculus     * 5. Number Theory
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v. Number theory           * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]]
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vi. High school algebra / trigonometry / precalculus           * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]]
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vii. Probability     * 9. About this document ...
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viii. Statistics
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b. Plotting 2 and 3 dimensions
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c. Sage math functions (sage as calculator), sage constants == To Do ==
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d. Generate Classroom examples     * 1. Basics
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i. show (), latex()           * 1.3. Programming in Sage
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ii. matplotlab           * 1.4. Sage Devel Basics
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3) Demonstrate SAGE functionality:     * 2. Calculus
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a. Primes           * 2.2. Integral Calculus
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b. Random numbers           * 2.3. Multivariate Calculus
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c. Plotting           * 2.4. Taylor Series and Infinite Sums
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d. Interact           * 2.5. Differential Equations
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e. Sage data types     * 3. Linear Algebra
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f. Email(?)           * 3.1. Matrix Algebra
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4) Programming           * 3.2. Vector Spaces
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a. Types, casting, relevant Sage data types     * 4. Abstract Algebra
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b. Lists, tuples           * 4.2. Rings and Fields
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c. Control operators (if, then, else, logical operators, in, srange())     * 5. Number Theory
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d. Loops           * 5.2. Elementary Number Theory II
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i. For, in, srange(), range()           * 5.3. Cryptography
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e. Functions           * 5.4. Elliptic Curves
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f. Recursion           * 5.6. Automorphic Forms
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5) Topics           * 5.7. Quaternion Algebra
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a. Primes and factorization           * 5.8. Modular Forms
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i. Given a random number, is it a prime?     * 6. Combinatorics
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1. Modular division           * 6.1. Counting
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a. random()           * 6.2. Graph Theory
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b. Factor()     * 7. Geometry
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2. Euclidean algorithm     * 8. Statistics
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a. Recursion           * 8.1. Statistical Methods
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b. gcd()           * 8.2. Probability
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3. primality testing

a. for loops

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 for Newbies

Contents

  1. Sage for Newbies
    1. Done
    2. To Do

Done

To Do

  • 1. Basics
    • 1.3. Programming in Sage
    • 1.4. Sage Devel Basics
  • 2. Calculus
    • 2.2. Integral Calculus
    • 2.3. Multivariate Calculus
    • 2.4. Taylor Series and Infinite Sums
    • 2.5. Differential Equations
  • 3. Linear Algebra
    • 3.1. Matrix Algebra
    • 3.2. Vector Spaces
  • 4. Abstract Algebra
    • 4.2. Rings and Fields
  • 5. Number Theory
    • 5.2. Elementary Number Theory II
    • 5.3. Cryptography
    • 5.4. Elliptic Curves
    • 5.6. Automorphic Forms
    • 5.7. Quaternion Algebra
    • 5.8. Modular Forms
  • 6. Combinatorics
    • 6.1. Counting
    • 6.2. Graph Theory
  • 7. Geometry
  • 8. Statistics
    • 8.1. Statistical Methods
    • 8.2. Probability
    • 8.3. Finance

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