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The Advanced CNXML
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This is the final installment of my three part tutorial on the ...

This is the final installment of my three part tutorial on the CNXML language. It is currently valid for the most recent release of the 0.3 language. The keywords contain a list of the tags described in this tutorial. Along with the example code in this module there is also an example module that has been growing throughout the tutorial.

Subject:
Computer Science
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ricardo Radaelli-Sanchez
First-order Logic
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We replace long lists of particular statements with a few general statements, ...

We replace long lists of particular statements with a few general statements, involving the quantifiers "for all" and "there exists". We see how this changes our proofs, and rules of inference.

Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ian Barland
A Gentle Introduction to the Art of Mathematics
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This book is designed for the transition course between calculus and differential ...

This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable.

It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.

Subject:
Mathematics
Material Type:
Textbooks
Hexagonal Pattern of Beehives
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The goal of this task is to use geometry study the structure ...

The goal of this task is to use geometry study the structure of beehives. Beehives have a tremendous simplicity as they are constructed entirely of small, equally sized walls. In order to as useful as possible for the hive, the goal should be to create the largest possible volume using the least amount of materials. In other words, the ratio of the volume of each cell to its surface area needs to be maximized. This then reduces to maximizing the ratio of the surface area of the cell shape to its perimeter.

Subject:
Education
Mathematics
Geometry
Material Type:
Activities and Labs
Instructional Material
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Intro to Logic
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An introduction to reasoning with Proposition and First-order logic, with applications to ...

An introduction to reasoning with Proposition and First-order logic, with applications to computer science. Part of the TeachLogic Project (www.teachlogic.org).

Subject:
Computer Science
Material Type:
Full Course
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ian Barland
John Greiner
Matthias Felleisen
Moshe Vardi
Phokion Kolaitis
Missing Angle Puzzles
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This lesson lays some of the ground work for eventually writing two ...

This lesson lays some of the ground work for eventually writing two column proofs. In the lesson students use known geometric facts to solve for missing angles. Students are asked to identify the key concepts required for the solution and to record the a path for finding the measure of a particular angle. Key concepts include the sum of the measures of the interior angles of a triangle and quadrilateral, parallel line relationships, and what can and cannot be assumed from a drawing.

Subject:
Geometry
Material Type:
Homework and Assignments
Lecture Notes
Provider:
Individual Authors
Provider Set:
Individual Authors
Author:
Jeff Holcomb
Propositional Logic
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Reducing statements to true/false propositions allows us to make precise statements, and ...

Reducing statements to true/false propositions allows us to make precise statements, and to make precise arguments which can be checked automatically.

Subject:
Philosophy
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ian Barland
Propositional Logic: partIIm
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More examples using formal proofs (inference rules) for determining whether a formula ...

More examples using formal proofs (inference rules) for determining whether a formula is true.

Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ian Barland
John Greiner
Matthias Felleisen
Moshe Vardi
Phokion Kolaitis
Pythagoras Theorem Proof
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An interactive applet and associated web page that demonstrates a graphical proof ...

An interactive applet and associated web page that demonstrates a graphical proof of Pythagoras' Theorem. The applet shows a right triangle that is replicated and then moved around to demonstrate the relationship between the sides. It can can be stepped through slowly to allow classroom discussion, or let to run as a movie. Useful for students who like to see things graphically as opposed to symbolically. Applet can be enlarged to full screen size for use with a classroom projector. This resource is a component of the Math Open Reference Interactive Geometry textbook project at http://www.mathopenref.com.

Subject:
Geometry
Material Type:
Readings
Simulations
Provider:
Math Open Reference
Provider Set:
Math Open Reference
Author:
John Page
Relational Logic
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We generalize from having a mass of propositional variables to representing the ...

We generalize from having a mass of propositional variables to representing the same information with relations. This prompts a few changes in notation and rules of inference.

Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Ian Barland
Seven Circles I
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This task is intended to help model a concrete situation with geometry. ...

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

Subject:
Education
Mathematics
Geometry
Trigonometry
Material Type:
Activities and Labs
Instructional Material
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
A Spiral Workbook for Discrete Mathematics
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This is a text that covers the standard topics in a sophomore-level ...

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

Subject:
Mathematics
Functions
Numbers and Operations
Material Type:
Textbooks
Provider:
State University of New York
Provider Set:
OpenSUNY Textbooks
Author:
Harris Kwong, SUNY Fredonia
The Superhyperbolic (Superultramodern) Doubt
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The superhyperbolic doubt is the principle that "anything may be possible", for ...

The superhyperbolic doubt is the principle that "anything may be possible", for that which could otherwise be believed to be absolutely (or 100%) certainly impossible at present could be possible as the intellectual capacities of the believer may be limited. That is, the proposition/s, for example, that are otherwise thought to be absolutely certainly true could be false. The superhyperbolic doubt is compared and attempted to shown to be superior to the hyperbolic Cartesian doubt and the idea/proposition that ‘anything is possible'. Furthermore, its implications are stated and discussed, the implications like ‘all axioms as 99.99% certainly true' and ‘all mathematics as philosophy'. Since the superhyperbolic doubt is the first and the most basic principle of my superultramodern science and philosophy, it could also be referred to as the superultramodern doubt.

Subject:
Philosophy
Material Type:
Readings
Syllabi
Provider:
Rice University
Provider Set:
Connexions
Author:
Kedar Joshi