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Major Goals:		 = Sage for Newbies =
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1. SAGE as a Smart Calculator (target: Freshmen) <<TableOfContents>>
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2. SAGE Primers / Tutorials for == Done ==
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(a) Quadratic Forms (target: Arizona Winter School Participants)     * 0. Front Matter
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(b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)     * 1. Basics
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(c) Number Theory via Primes (target: Elementary Number Theory students)           * 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]]
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(d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]           * 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]]
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(e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner]     * 2. Calculus
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(f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]           * 2.1. Differential Calculus [[attachment:differential_calculus.sws]]

    * 4. Abstract Algebra

          * 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer)

    * 5. Number Theory

          * 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]]

          * 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]]

    * 9. About this document ...
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Typesetting:		 == To Do ==
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    * 1. Basics
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reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]           * 1.3. Programming in Sage
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          * 1.4. Sage Devel Basics
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    * 2. Calculus
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          * 2.2. Integral Calculus
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-------------           * 2.3. Multivariate Calculus
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Goals:           * 2.4. Taylor Series and Infinite Sums
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1) Accessible to high school math teachers and undergraduate mathematics majors.           * 2.5. Differential Equations
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2) Anticipated user desires     * 3. Linear Algebra
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a. Content specific modules           * 3.1. Matrix Algebra
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i. Quadratic Forms           * 3.2. Vector Spaces
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ii. Group theory     * 4. Abstract Algebra
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iii. Abstract algebra           * 4.2. Rings and Fields
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iv. Calculus     * 5. Number Theory
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v. Number theory           * 5.2. Elementary Number Theory II
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vi. High school algebra / trigonometry / precalculus           * 5.3. Cryptography
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vii. Probability           * 5.4. Elliptic Curves
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viii. Statistics           * 5.6. Automorphic Forms
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b. Plotting 2 and 3 dimensions           * 5.7. Quaternion Algebra
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c. Sage math functions (sage as calculator), sage constants           * 5.8. Modular Forms
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d. Generate Classroom examples     * 6. Combinatorics
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i. show (), latex()           * 6.1. Counting
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ii. matplotlab           * 6.2. Graph Theory
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3) Demonstrate SAGE functionality:     * 7. Geometry
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a. Primes     * 8. Statistics
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b. Random numbers           * 8.1. Statistical Methods
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c. Plotting           * 8.2. Probability
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d. Interact

e. Sage data types

f. Email(?)

4) Programming

a. Types, casting, relevant Sage data types

b. Lists, tuples

c. Control operators (if, then, else, logical operators, in, srange())

d. Loops

i. For, in, srange(), range()

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 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)