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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 | == Major Goals : Sage Primers == |
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| (a) Quadratic Forms (target: Arizona Winter School Participants) | === Basics === |
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| * SAGE as a Smart Calculator (target: Freshmen) [[attachment:Sage_as_a_Smart_Calculator_0.3.sws]] [[attachment:Sage_as_a_Smart_Calculator_0.4.sws]] | |
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| (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students) | 2. SAGE Primers |
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| (a) Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] | |
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| (c) Number Theory via Primes (target: Elementary Number Theory students) | (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students) |
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| (c) Number Theory via Primes (target: Elementary Number Theory students) | |
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| (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer] | (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer] |
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| (e) Differential Calculus (target: Freshmen) [[attachment:Differential_Calculus_Primer_0.3.sws]] |
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| (e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner] | (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] |
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| (g) Primer guidelines [[attachment:primer_template\example.sws]] | |
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| (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein] |
(3) Primer Design Principles [[attachment:primer_design_principles.rtf]] |
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f. Email(?) |
Sage for Newbies
<<TableofContents>>
Major Goals : Sage Primers
Basics
SAGE as a Smart Calculator (target: Freshmen) Sage_as_a_Smart_Calculator_0.3.sws Sage_as_a_Smart_Calculator_0.4.sws
2. SAGE Primers
(a) Quadratic Forms (target: Arizona Winter School Participants) quadratic_forms.sws
(b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)
(c) Number Theory via Primes (target: Elementary Number Theory students)
(d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]
(e) Differential Calculus (target: Freshmen) Differential_Calculus_Primer_0.3.sws
(f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]
(g) Primer guidelines primer_template\example.sws
(3) Primer Design Principles primer_design_principles.rtf
Typesetting:
reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]
Goals:
1) Accessible to high school math teachers and undergraduate mathematics majors.
2) Anticipated user desires
a. Content specific modules
i. Quadratic Forms
ii. Group theory
iii. Abstract algebra
iv. Calculus
v. Number theory
vi. High school algebra / trigonometry / precalculus
vii. Probability
viii. Statistics
b. Plotting 2 and 3 dimensions
c. Sage math functions (sage as calculator), sage constants
d. Generate Classroom examples
i. show (), latex()
ii. matplotlab
3) Demonstrate SAGE functionality:
a. Primes
b. Random numbers
c. Plotting
d. Interact
e. Sage data types
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 (?)