Sage for Newbies
Contents
Major Goals : Sage Primers
Basics
Primer Guidelines primer_template\example.sws
Primer Design Principles primer_design_principles.rtf
SAGE as a Smart Calculator (target: Freshmen) sage_as_a_smart_calculator.sws
Calculus
Differential Calculus (target: Freshmen) differential_calculus.sws
- Integral Calculus (target: Freshmen)
Number Theory
Quadratic Forms (target: Arizona Winter School Participants) quadratic_forms.sws
- Number Theory via Diophantine Equations (target: Elementary Number Theory students)
Number Theory via Primes (target: Elementary Number Theory students) number_theory.primes_0.1.sws
Abstract Algebra
Group Theory by Robert Beezer (target: Undergraduate Math Majors) group_theory.sws
Target
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 (?)