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Ancient Greek Philosophy and Mathematics
Conditional Remix & Share Permitted
CC BY-NC-SA
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This course explores the relationship between ancient Greek philosophy and mathematics. We investigate how ideas of definition, reason, argument and proof, rationality / irrationality, number, quality and quantity, truth, and even the idea of an idea were shaped by the interplay of philosophic and mathematical inquiry. The course examines how discovery of the incommensurability of magnitudes challenged the Greek presumption that the cosmos is fully understandable. Students explore the influence of mathematics on ancient Greek ethical theories. We read such authors as: Euclid, Plato, Aristotle, Nicomachus, Theon of Smyrna, Bacon, Descartes, Dedekind, and Newton.

Subject:
Ancient History
Arts and Humanities
English Language Arts
History
Literature
Mathematics
Philosophy
Reading Literature
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Perlman, Lee
Date Added:
02/01/2016
Discrete Mathematics: An Open Introduction
Conditional Remix & Share Permitted
CC BY-SA
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Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math majors, especially those who will go on to teach. The textbook has been developed while teaching the Discrete Mathematics course at the University of Northern Colorado. Primitive versions were used as the primary textbook for that course since Spring 2013, and have been used by other instructors as a free additional resource. Since then it has been used as the primary text for this course at UNC, as well as at other institutions.

Subject:
Mathematics
Material Type:
Textbook
Author:
Oscar Levin
Date Added:
11/21/2018
A Gentle Introduction to the Art of Mathematics
Read the Fine Print
Some Rights Reserved
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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:
Textbook
Provider:
Southern Connecticut State University
Date Added:
02/19/2015
Hexagonal Pattern of Beehives
Unrestricted Use
CC BY
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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:
Geometry
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
01/21/2013
Mathematical Reasoning Writing and Proof, Version 3
Conditional Remix & Share Permitted
CC BY-NC-SA
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Mathematical Reasoning: Writing and Proof is a text for the first college mathematics course that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. Version 3 of this book is almost identical to Version 2.1. The main change is that the preview activities in Version 2.1 have been renamed to beginning activities in Version 3. This was done to emphasize that these activities are meant to be completed before starting the rest of the section and are not just a short preview of what is to come in the rest of the section.

Subject:
Mathematics
Material Type:
Textbook
Provider:
Grand Valley State University
Date Added:
03/24/2020
A Primer of Real Analysis
Conditional Remix & Share Permitted
CC BY-NC-SA
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This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.

Subject:
Mathematics
Material Type:
Textbook
Author:
Dan Sloughter
Date Added:
11/20/2018
The Pythagorean Theorem:  Geometry's Most Elegant Theorem
Conditional Remix & Share Permitted
CC BY-NC-SA
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This lesson teaches students about the history of the Pythagorean theorem, along with proofs and applications. It is geared toward high school Geometry students that have completed a year of Algebra.

Subject:
Geometry
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Date Added:
07/12/2014
Seven Circles I
Unrestricted Use
CC BY
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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:
Geometry
Mathematics
Trigonometry
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/20/2012
A Spiral Workbook for Discrete Mathematics
Conditional Remix & Share Permitted
CC BY-NC-SA
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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:
Applied Science
Computer Science
Functions
Mathematics
Numbers and Operations
Material Type:
Textbook
Provider:
State University of New York
Provider Set:
Milne Open Textbooks
Author:
Harris Kwong
Date Added:
11/06/2015