Differences between revisions 27 and 46 (spanning 19 versions)

Sage Primers

Contents

Sage Primers
1. Done / In Progress
2. To Do

Done / In Progress

0. Sage Primer Design Principles Sage Primer Design Principles.pdf primer_design_principles.rtf
1. Basics
- 1.1. Primer Template: An Example primer_template_example.sws
- 1.2. Sage as a Smart Calculator basics.smart_calculator_0.5.sws
- 1.4. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified.
2. Calculus
- 2.1. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.2. Integral Calculus [Sourav]
3. Linear Algebra
- 3.1. Matrix Algebra [Sourav]
4. Abstract Algebra
- 4.1. Group Theory group_theory.sws (by Robert Beezer)
5. Number Theory
- 5.1. Elementary Number Theory I number_theory.primes_0.5.sws
- 5.2. Elementary Number Theory II [Erik]
- 5.5. Quadratic Forms quadratic_forms.sws
- 5.7. Quaternion Algebra [Sourav]
9. About this document ...

To Do

1. Basics
- 1.3. Programming in Sage
- 1.5. 2D and 3D Plotting in Sage
- 1.6. Interact in Sage [Erik]
2. Calculus
- 2.3. Multivariate Calculus
- 2.4. Taylor Series and Infinite Sums
- 2.5. Differential Equations
3. Linear Algebra
- 3.2. Vector Spaces [Sourav]
4. Abstract Algebra
- 4.2. Rings and Fields [Erik]
5. Number Theory
- 5.3. Cryptography [Dan]
- 5.4. Elliptic Curves [Aly]
- 5.6. Automorphic Forms
- 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

-  ⇤ ← Revision 27 as of 2009-03-02 05:16:44 → 
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  Editor: SouravSenGupta
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+   ← Revision 46 as of 2009-03-11 14:06:24 → ⇥
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+Additions are marked like this.
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-= Sage for Newbies =
+= Sage Primers =
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-<<TableofContents>>

== Major Goals : Sage Primers ==

=== Basics ===

 * 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]]

2. SAGE Primers

(a) Quadratic Forms (target: Arizona Winter School Participants) [[attachment: 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)
[[attachment: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 [[attachment:primer_template\example.sws]]

(3) Primer Design Principles [[attachment:primer_design_principles.rtf]]
+<<TableOfContents>>
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-------------
Typesetting:
+== Done / In Progress ==
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+    * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
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+Line 10:
-reSTRUCTUREDtext [http://docutils.sourceforge.net/rst.html]
+    * 1. Basics

          * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]] 

          * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]

          * 1.4. Sage Devel Basics [Erik, Aly] [[attachment:dev_for_newbies.html]]-this needs to be restified.

    * 2. Calculus

          * 2.1. Differential Calculus [[attachment:calculus.differential_calculus_1.0.sws]]

          * 2.2. Integral Calculus [Sourav]

    * 3. Linear Algebra

          * 3.1. Matrix Algebra [Sourav]

    * 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_0.5.sws]]

          * 5.2. Elementary Number Theory II [Erik]

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

          * 5.7. Quaternion Algebra [Sourav]

    * 9. About this document ...
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+Line 46:
+== To Do ==
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--------------
+    * 1. Basics
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+Line 50:
-Goals:
+          * 1.3. Programming in Sage
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-)	Accessible to high school math teachers and undergraduate mathematics majors.
+          * 1.5. 2D and 3D Plotting in Sage
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+Line 54:
-)	Anticipated user desires
+          * 1.6. Interact in Sage [Erik]
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+Line 56:
-a.	Content specific modules
+    * 2. Calculus
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+Line 58:
-i.	Quadratic Forms
+          * 2.3. Multivariate Calculus
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+Line 60:
-ii.	Group theory
+          * 2.4. Taylor Series and Infinite Sums
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+Line 62:
-iii.	Abstract algebra
+          * 2.5. Differential Equations
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+Line 64:
-iv.	Calculus
+    * 3. Linear Algebra
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+Line 66:
-v.	Number theory
+          * 3.2. Vector Spaces [Sourav]
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+Line 68:
-vi.	High school algebra / trigonometry / precalculus
+    * 4. Abstract Algebra
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+Line 70:
-vii.	Probability
+          * 4.2. Rings and Fields [Erik]
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+Line 72:
-viii.	Statistics
+    * 5. Number Theory
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+Line 74:
-b.	Plotting 2 and 3 dimensions
+          * 5.3. Cryptography [Dan]
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-c.	Sage math functions (sage as calculator), sage constants
+          * 5.4. Elliptic Curves [Aly]
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-d.	Generate Classroom examples
+          * 5.6. Automorphic Forms
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-i.	show (), latex()
+          * 5.8. Modular Forms
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-ii.	matplotlab
+    * 6. Combinatorics
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-)	Demonstrate SAGE functionality:
+          * 6.1. Counting
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-a.	Primes
+          * 6.2. Graph Theory
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-b.	Random numbers
+    * 7. Geometry
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-c.	Plotting
+    * 8. Statistics
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-d.	Interact
+          * 8.1. Statistical Methods [Erik]
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-e.	Sage data types
+          * 8.2. Probability [Erik]
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-)	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

Diff for "days13/projects/sagenewbie"

Sage Primers

Done / In Progress

To Do