Differences between revisions 10 and 63 (spanning 53 versions)

Sage Primers

Contents

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

Todo: Polish up these primers and put them in the Sage Constructions document.

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
- 1.3. Basic 2D plotting with Sage Ploting_with_Sage_v1.0.1.sws by Jose Guzman
- 1.4. Solving basic equations with Sage Ball_motion.sws by Jose Guzman
- 1.5. Sage Devel Basics [Erik, Aly] dev_for_newbies.html-this needs to be restified., development_for_newbies.sws
2. Calculus
- 2.1. Limits Calculus Analysis_tutorial_Limits_v1.0.2.sws by Jose Guzman
- 2.2. Differential Calculus calculus.differential_calculus_1.0.sws
- 2.3. 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 [Erik] number_theory.primes_diophantine_equations.1.0.sws
- 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 [JoseGuzman]
- 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 10 as of 2009-03-01 03:15:23 → 
  Size: 2647
  Editor: SouravSenGupta
  Comment:
+   ← Revision 63 as of 2011-01-06 14:54:28 → ⇥
  Size: 2909
  Editor: Valod Malod
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
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-------------
Major Goals:
+= Sage Primers =
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-. SAGE as a Smart Calculator (target: Freshmen)
+<<TableOfContents>>
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-. SAGE Primers / Tutorials for
+'''Todo:''' Polish up these primers and put them in the [[http://www.sagemath.org/doc/constructions/|Sage Constructions]] document.
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-    (a) Quadratic Forms (target: Arizona Winter School Participants)\n
+== Done / In Progress ==
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+Line 9:
-    (b) Number Theory via Diophantine Equations (target: Elementary Number Theory students)\n
+    * 0. Sage Primer Design Principles [[attachment:Sage Primer Design Principles.pdf]] [[attachment:primer_design_principles.rtf]]
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+Line 11:
-    (c) Number Theory via Primes (target: Elementary Number Theory students)
+    * 1. Basics
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+Line 13:
-    (d) Group Theory (target: Undergraduate Math Majors) [http://abstract.ups.edu/sage-aata.html by Rob Beezer]
+          * 1.1. Primer Template: An Example [[attachment:primer_template_example.sws]]
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+Line 15:
-    (e) Differential Calculus (target: Freshmen) [http://sage.math.washington.edu/home/wdj/teaching/calc1-sage/ by David Joyner]
+          * 1.2. Sage as a Smart Calculator [[attachment:basics.smart_calculator_0.5.sws]]
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+Line 17:
-    (f) Integral Calculus (target: Freshmen) [http://wdjoyner.com/teach/calc2-sage/hoffman-stein-calculus.pdf by Hoffman, Joyner & Stein]
+          * 1.3. Basic 2D plotting with Sage [[attachment:Ploting_with_Sage_v1.0.1.sws]] by Jose Guzman

          * 1.4. Solving basic equations with Sage [[attachment:Ball_motion.sws]] by Jose Guzman

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

    * 2. Calculus

          * 2.1. Limits Calculus [[attachment:Analysis_tutorial_Limits_v1.0.2.sws]] by Jose Guzman

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

          * 2.3. 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 [Erik] [[attachment:number_theory.primes_diophantine_equations.1.0.sws]]

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

          * 5.7. Quaternion Algebra [Sourav]

    * 9. About this document ...
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+Line 51:
-------------
Typesetting:
+== To Do ==

    * 1. Basics

          * 1.3. Programming in Sage

          * 1.5. 2D and 3D Plotting in Sage [JoseGuzman]

          * 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
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+Line 104:
-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

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 (?)
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Diff for "days13/projects/sagenewbie"

Sage Primers

Done / In Progress

To Do