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| == Major Goals : Sage Primers == | == Done == |
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| === Basics === | * 0. Front Matter * 1. Basics o 1.1. Primer Template: An Example [[attachment:primer_template\example.sws]] [[attachment:primer_design_principles.rtf]] o 1.2. Sage as a Smart Calculator [[attachment:sage_as_a_smart_calculator.sws]] * 2. Calculus o 2.1. Differential Calculus [[attachment:differential_calculus.sws]] * 4. Abstract Algebra o 4.1. Group Theory [[attachment:group_theory.sws]] (by Robert Beezer) * 5. Number Theory o 5.1. Elementary Number Theory I [[attachment: number_theory.primes_0.1.sws]] o 5.5. Quadratic Forms [[attachment: quadratic_forms.sws]] * 9. About this document ... |
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| * Primer Guidelines [[attachment:primer_template\example.sws]] | == To Do == |
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| * Primer Design Principles [[attachment:primer_design_principles.rtf]] * SAGE as a Smart Calculator (target: Freshmen) [[attachment:sage_as_a_smart_calculator.sws]] === Calculus === * Differential Calculus (target: Freshmen) [[attachment:differential_calculus.sws]] * Integral Calculus (target: Freshmen) === Number Theory === * Quadratic Forms (target: Arizona Winter School Participants) [[attachment: quadratic_forms.sws]] * Number Theory via Diophantine Equations (target: Elementary Number Theory students) * Number Theory via Primes (target: Elementary Number Theory students) [[attachment: number_theory.primes_0.1.sws]] === Abstract Algebra === * Group Theory by Robert Beezer (target: Undergraduate Math Majors) [[attachment: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 (?) |
* 1. Basics o 1.3. Programming in Sage o 1.4. Sage Devel Basics * 2. Calculus o 2.2. Integral Calculus o 2.3. Multivariate Calculus o 2.4. Taylor Series and Infinite Sums o 2.5. Differential Equations * 3. Linear Algebra o 3.1. Matrix Algebra o 3.2. Vector Spaces * 4. Abstract Algebra o 4.2. Rings and Fields * 5. Number Theory o 5.2. Elementary Number Theory II o 5.3. Cryptography o 5.4. Elliptic Curves o 5.6. Automorphic Forms o 5.7. Quaternion Algebra o 5.8. Modular Forms * 6. Combinatorics o 6.1. Counting o 6.2. Graph Theory * 7. Geometry * 8. Statistics o 8.1. Statistical Methods o 8.2. Probability o 8.3. Finance |
Sage for Newbies
Contents
Done
- 0. Front Matter
- 1. Basics
o 1.1. Primer Template: An Example primer_template\example.sws primer_design_principles.rtf o 1.2. Sage as a Smart Calculator sage_as_a_smart_calculator.sws
- 2. Calculus
o 2.1. Differential Calculus differential_calculus.sws
- 4. Abstract Algebra
o 4.1. Group Theory group_theory.sws (by Robert Beezer)
- 5. Number Theory
o 5.1. Elementary Number Theory I number_theory.primes_0.1.sws o 5.5. Quadratic Forms quadratic_forms.sws
- 9. About this document ...
To Do
- 1. Basics
- o 1.3. Programming in Sage o 1.4. Sage Devel Basics
- 2. Calculus
- o 2.2. Integral Calculus o 2.3. Multivariate Calculus o 2.4. Taylor Series and Infinite Sums o 2.5. Differential Equations
- 3. Linear Algebra
- o 3.1. Matrix Algebra o 3.2. Vector Spaces
- 4. Abstract Algebra
- o 4.2. Rings and Fields
- 5. Number Theory
- o 5.2. Elementary Number Theory II o 5.3. Cryptography o 5.4. Elliptic Curves o 5.6. Automorphic Forms o 5.7. Quaternion Algebra o 5.8. Modular Forms
- 6. Combinatorics
- o 6.1. Counting o 6.2. Graph Theory
- 7. Geometry
- 8. Statistics
- o 8.1. Statistical Methods o 8.2. Probability o 8.3. Finance