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= Sage for Newbies = = Sage Primers =
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== Major Goals : Sage Primers == == Done ==
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=== Basics ===     * 0. Front Matter
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 * Primer Guidelines [[attachment:primer_template\example.sws]]     * 1. Basics
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 * Primer Design Principles [[attachment:primer_design_principles.rtf]]           * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]]
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 * SAGE as a Smart Calculator (target: Freshmen) [[attachment:sage_as_a_smart_calculator.sws]]           * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
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=== Calculus ===     * 2. Calculus
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 * Differential Calculus (target: Freshmen) [[attachment:differential_calculus.sws]]           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]
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 * Integral Calculus (target: Freshmen)     * 4. Abstract Algebra
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=== Number Theory ===           * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)
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 * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]]     * 5. Number Theory
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 * Number Theory via Diophantine Equations (target: Elementary Number Theory students)           * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]]
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 * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]]           * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]]
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=== Abstract Algebra ===

 * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment:group_theory.sws]]		     * 9. About this document ...
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== Target ==
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1) Accessible to high school math teachers and undergraduate mathematics majors. == To Do ==
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2) Anticipated user desires     * 1. Basics
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a. Content specific modules           * 1.3. Programming in Sage
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i. Quadratic Forms           * 1.4. Sage Devel Basics [Erik, Aly, Sourav]
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ii. Group theory     * 2. Calculus
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iii. Abstract algebra           * 2.2. Integral Calculus [Sourav]
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iv. Calculus           * 2.3. Multivariate Calculus
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v. Number theory           * 2.4. Taylor Series and Infinite Sums
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vi. High school algebra / trigonometry / precalculus           * 2.5. Differential Equations
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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           * 3.2. Vector Spaces [Sourav]
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c. Sage math functions (sage as calculator), sage constants     * 4. Abstract Algebra
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d. Generate Classroom examples           * 4.2. Rings and Fields [Erik]
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i. show (), latex()     * 5. Number Theory
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ii. matplotlab           * 5.2. Elementary Number Theory II [Erik]
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3) Demonstrate SAGE functionality:           * 5.3. Cryptography [Dan]
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a. Primes           * 5.4. Elliptic Curves [Aly]
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b. Random numbers           * 5.6. Automorphic Forms
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c. Plotting           * 5.7. Quaternion Algebra [Aly, Sourav]
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d. Interact           * 5.8. Modular Forms
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e. Sage data types     * 6. Combinatorics
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4) Programming           * 6.1. Counting
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a. Types, casting, relevant Sage data types           * 6.2. Graph Theory
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b. Lists, tuples     * 7. Geometry
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c. Control operators (if, then, else, logical operators, in, srange())     * 8. Statistics
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d. Loops           * 8.1. Statistical Methods [Erik]
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i. For, in, srange(), range()           * 8.2. Probability [Erik]
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e. Functions

f. Recursion

5) Topics

a. Primes and factorization

i. Given a random number, is it a prime?

1. Modular division

a. random()

b. Factor()

2. Euclidean algorithm

a. Recursion

b. gcd()

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 Primers

Contents

  1. Sage Primers
    1. Done
    2. To Do

Done

To Do

  • 1. Basics
    • 1.3. Programming in Sage
    • 1.4. Sage Devel Basics [Erik, Aly, Sourav]
  • 2. Calculus
    • 2.2. Integral Calculus [Sourav]
    • 2.3. Multivariate Calculus
    • 2.4. Taylor Series and Infinite Sums
    • 2.5. Differential Equations
  • 3. Linear Algebra
    • 3.1. Matrix Algebra [Sourav]
    • 3.2. Vector Spaces [Sourav]
  • 4. Abstract Algebra
    • 4.2. Rings and Fields [Erik]
  • 5. Number Theory
    • 5.2. Elementary Number Theory II [Erik]
    • 5.3. Cryptography [Dan]
    • 5.4. Elliptic Curves [Aly]
    • 5.6. Automorphic Forms
    • 5.7. Quaternion Algebra [Aly, Sourav]
    • 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)