From 045ac004bc140ad51289fba2441c80e14e85d6be Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Tue, 7 May 2024 23:47:40 +0000 Subject: [PATCH 01/14] Add set theory intro --- source/set-theory/ch-set-theory.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/set-theory/ch-set-theory.ptx b/source/set-theory/ch-set-theory.ptx index 63edf62f..9046f811 100644 --- a/source/set-theory/ch-set-theory.ptx +++ b/source/set-theory/ch-set-theory.ptx @@ -4,7 +4,9 @@ Set Theory -

Set theory is a fundamental branch of mathematical logic that deals with the properties and relations of sets, which are collections of objects. Developed in the late 19th century by Georg Cantor, set theory provides the foundational framework for nearly all of mathematics. It introduces the concept of infinite sets, explores the sizes of these sets, and examines operations between them. Essential to understanding mathematical structures, set theory is not only pivotal in pure mathematics but also has applications in computer science, philosophy, and linguistics. This introduction covers the basic principles and operations of set theory, providing a solid foundation for further mathematical exploration.

+

+ This chapter presents the study of set theory with Sage, starting with a description of the Set function and its variations, then how to use it to calculate the basic set operations. +

From d6f29423ed54a191d699f963e53bb9597bf9b6c8 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Tue, 7 May 2024 23:50:22 +0000 Subject: [PATCH 02/14] Correct set definitions title --- source/set-theory/sec-creating-sets.ptx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/set-theory/sec-creating-sets.ptx b/source/set-theory/sec-creating-sets.ptx index 97ceb0b8..9a1ddd5d 100644 --- a/source/set-theory/sec-creating-sets.ptx +++ b/source/set-theory/sec-creating-sets.ptx @@ -4,7 +4,7 @@ Creating Sets - Sage Math Set + Set Definitions

To construct a set, encase the elements within square brackets []. Then, pass this list as an argument to the Set() function. It's important to note that the S in Set() should be uppercase to define a Sage set. In a set, each element is unique.

From 1f58d97c7ca34bccfffd0d6dedadacbf325c004b Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 04:48:04 +0000 Subject: [PATCH 03/14] Add Combinatorics intro --- source/combinatorics/ch-combinatorics.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/combinatorics/ch-combinatorics.ptx b/source/combinatorics/ch-combinatorics.ptx index d5b59444..248591ed 100644 --- a/source/combinatorics/ch-combinatorics.ptx +++ b/source/combinatorics/ch-combinatorics.ptx @@ -4,7 +4,9 @@ Combinatorics -

Combinatorics introduction paragraph here

+

+ Counting techniques arise naturally in computer algebra as well as in basic applications in daily life. This chapter covers the treatment in Sage of the enumeration problem, like counting combinations and counting permutations as well as listing them. +

From f4fc554a1fcf1e5f4d4c5f8a441a4572eda7e4a0 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 04:51:38 +0000 Subject: [PATCH 04/14] Add logic intro --- source/logic/ch-logic.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/logic/ch-logic.ptx b/source/logic/ch-logic.ptx index 2e926ca5..0da7184a 100644 --- a/source/logic/ch-logic.ptx +++ b/source/logic/ch-logic.ptx @@ -4,7 +4,9 @@ Logic -

Logic introduction paragraph here

+

+ In this chapter, we introduce different ways to create boolean formulas using the logical functions not, and, or, if then, and iff. Then, we show how to ask Sage to create a truth table from a formula and determine if an expression is a contradiction or a tautology. +

From 2b19c05b1c2fdffdd743a72aea52fc5867e03eaf Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:03:43 +0000 Subject: [PATCH 05/14] Add relations intro --- source/relations/ch-relations.ptx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/relations/ch-relations.ptx b/source/relations/ch-relations.ptx index d78d46a9..59c34ffa 100644 --- a/source/relations/ch-relations.ptx +++ b/source/relations/ch-relations.ptx @@ -5,7 +5,7 @@

- Now that we've studied sets, its time to investigate the interrelationships between the elements of a set. + Building on the Cartesian product introduced earlier, this chapter deals with relations between the elements in sets. We will first see how to visualize with Sage some relations and then we introduce some new functions to decide if they are equivalence or partial order relations.

From e8d55e4b9964e0a2d7310ef899232670694e4204 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:04:32 +0000 Subject: [PATCH 06/14] Update relations intro --- source/relations/ch-relations.ptx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/relations/ch-relations.ptx b/source/relations/ch-relations.ptx index 59c34ffa..8a60aa97 100644 --- a/source/relations/ch-relations.ptx +++ b/source/relations/ch-relations.ptx @@ -5,7 +5,7 @@

- Building on the Cartesian product introduced earlier, this chapter deals with relations between the elements in sets. We will first see how to visualize with Sage some relations and then we introduce some new functions to decide if they are equivalence or partial order relations. + In this chapter, we'll explore the relationships between elements in sets, building upon the concept of "Cartesian product" introduced earlier. We'll begin by learning how to visualize relations using Sage. Then, we'll introduce some new functions that can help us determine whether these relations are equivalence or partial order relations.

From 4058e94e3da611b8e31f42b1851b165893bec964 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:05:38 +0000 Subject: [PATCH 07/14] Add functions intro --- source/functions/ch-functions.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/functions/ch-functions.ptx b/source/functions/ch-functions.ptx index e1b9d05e..95131d50 100644 --- a/source/functions/ch-functions.ptx +++ b/source/functions/ch-functions.ptx @@ -4,7 +4,9 @@ Functions -

Functions introduction paragraph here

+

+ This chapter will discuss briefly the implementation of functions in Sage and delve deeper into the sequences defined by recursion, including the Fibonacci one. We show how to solve a recurrence relation using Sage. +

From ba7567c89928e4ee47e22e9340fec02f0716c232 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:14:42 +0000 Subject: [PATCH 08/14] Add graph theory intro --- source/graph-theory/ch-graph-theory.ptx | 39 +------------------------ 1 file changed, 1 insertion(+), 38 deletions(-) diff --git a/source/graph-theory/ch-graph-theory.ptx b/source/graph-theory/ch-graph-theory.ptx index 01b56ef1..e8cb493d 100644 --- a/source/graph-theory/ch-graph-theory.ptx +++ b/source/graph-theory/ch-graph-theory.ptx @@ -5,44 +5,7 @@

- Applications of graphs include: -

    -
  • -

    - Social interaction -

    -
    • -
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    - Influence -

    -
    • -
  • -

    - Call network -

    -
    • -
  • -

    - World wide web -

    -
    • -
  • -

    - Citation graph -

    -
    • -
  • -

    - Collaboration -

    -
    • -
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    - PageRank -

    -
    • -
+ Sage is extremely powerful for graph theory. This chapter presents the study of graph theory with Sage, starting with a description of the Graph class through the implementation of optimization algorithms. We also illustrate Sage's graphical capabilities for visualizing graphs.

From edaca88c2e1c55f157054d6cb068c52b8a9c84d7 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:23:30 +0000 Subject: [PATCH 09/14] Add trees intro --- source/trees/ch-trees.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/trees/ch-trees.ptx b/source/trees/ch-trees.ptx index 8fed470e..0dc12e20 100644 --- a/source/trees/ch-trees.ptx +++ b/source/trees/ch-trees.ptx @@ -4,7 +4,9 @@ Trees -

Trees introduction paragraph here

+

+ This chapter completes the preceding one by explaining how to ask Sage to decide whether a given graph is a tree and then introduce further searching algorithms for trees. +

From 00112e54d48b861f4027794d90e15d0531305380 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:24:08 +0000 Subject: [PATCH 10/14] Add lattices intro --- source/lattices/ch-lattices.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/lattices/ch-lattices.ptx b/source/lattices/ch-lattices.ptx index cfdc99a9..4000a40d 100644 --- a/source/lattices/ch-lattices.ptx +++ b/source/lattices/ch-lattices.ptx @@ -4,7 +4,9 @@ Lattices -

Lattice introduction paragraph here

+

+ Building on the partial order sets introduced earlier, this chapter explains how to ask Sage to decide whether a given poset is a lattice. Then we show how to calculate the meet and join tables using build-in functions in Sage as well as customized ones. +

From 4d9d7b3bd7aa3c1019aef856fb75669596822ff7 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:26:41 +0000 Subject: [PATCH 11/14] Update lattices intro --- source/lattices/ch-lattices.ptx | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/source/lattices/ch-lattices.ptx b/source/lattices/ch-lattices.ptx index 4000a40d..9632c7a5 100644 --- a/source/lattices/ch-lattices.ptx +++ b/source/lattices/ch-lattices.ptx @@ -5,7 +5,7 @@

- Building on the partial order sets introduced earlier, this chapter explains how to ask Sage to decide whether a given poset is a lattice. Then we show how to calculate the meet and join tables using build-in functions in Sage as well as customized ones. + This chapter builds on the partial order sets introduced earlier and explains how to ask Sage to decide whether a given poset is a lattice. Then, we show how to calculate the meet and join tables using built-in and customized Sage functions.

From b3dba2f4340dbf37d3e660ed553f8a1659eb6606 Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 05:28:00 +0000 Subject: [PATCH 12/14] Add boolean algebra intro --- source/boolean-algebra/ch-boolean-algebra.ptx | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/source/boolean-algebra/ch-boolean-algebra.ptx b/source/boolean-algebra/ch-boolean-algebra.ptx index ba12505f..0e64203f 100644 --- a/source/boolean-algebra/ch-boolean-algebra.ptx +++ b/source/boolean-algebra/ch-boolean-algebra.ptx @@ -4,7 +4,9 @@ Boolean Algebra -

Boolean algebra introduction paragraph here

+

+ This chapter completes the preceding one by explaining how to ask Sage to decide whether a given lattice is a Boolean algebra. We also illustrate basic operations with Boolean functions. +

From 48824aa53e255cb55f67a59101fdb4215dbf467d Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 06:29:06 +0000 Subject: [PATCH 13/14] Update defining functions to include variables --- source/getting-started/sec-defining-functions.ptx | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/source/getting-started/sec-defining-functions.ptx b/source/getting-started/sec-defining-functions.ptx index 600c473d..6d811b3f 100644 --- a/source/getting-started/sec-defining-functions.ptx +++ b/source/getting-started/sec-defining-functions.ptx @@ -23,7 +23,9 @@ # Replace 'World' with your name - greetings('World') + your_name = 'World' + + greetings(your_name)

@@ -45,7 +47,8 @@

- greetings('') + no_name = '' + greetings(no_name) @@ -60,9 +63,7 @@ def greetings(name): """ - Generate a greeting message for a given name. - - This function takes a name as input and returns a greeting string. It ensures the name is a string and not empty, raising a ValueError with an appropriate message if these conditions are not met. + This function takes a name and returns a greeting. It ensures the name is a string and not empty, raising a ValueError with a message if these conditions are not met. Parameters: - name (str): The name to include in the greeting. From 59c4a1ff406e3f7aff038d49759714ade519d16b Mon Sep 17 00:00:00 2001 From: Samuel Lubliner Date: Wed, 8 May 2024 06:37:06 +0000 Subject: [PATCH 14/14] Add notes to function --- source/getting-started/sec-defining-functions.ptx | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/source/getting-started/sec-defining-functions.ptx b/source/getting-started/sec-defining-functions.ptx index 6d811b3f..a3df2692 100644 --- a/source/getting-started/sec-defining-functions.ptx +++ b/source/getting-started/sec-defining-functions.ptx @@ -11,6 +11,12 @@

Here we have a function that takes a name as an argument and returns a greeting:

+ def greetings(name):