Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-28T23:13:20.471Z Has data issue: false hasContentIssue false
This chapter is part of a book that is no longer available to purchase from Cambridge Core

III - May

from Appendices

Charles A. Coppin ,
W. Ted Mahavier ,
E. Lee May  and
G. Edgar Parker
Charles A. Coppin
Affiliation:
Lamar University
W. Ted Mahavier
Affiliation:
Lamar University
E. Lee May
Affiliation:
Salisbury University
G. Edgar Parker
Affiliation:
James Madison University
Get access

Summary

Syllabus for Introduction to Abstract Mathematics

SALISBURY UNIVERSITY

DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE

SYLLABUS (Tentative)

MATH 300 Introduction to Abstract Mathematics

Intended Audience: Students minoring in mathematics, particularly prospective teachers, will find this a good capstone to their undergraduate mathematical experience. Students majoring in mathematics who have not already completed a 400-level mathematics course will find this a valuable course to help them develop a better understanding of the connection between computational and theoretical mathematics.

Objective: To provide students with an opportunity to develop the foundations of abstract mathematics in a manner similar to that employed by professional mathematicians.

Prerequisite: Discrete Mathematics, completed with a grade of C or better.

Text: Notes distributed by the instructor.

Foundations, I: The Theory of Sets (2 weeks)

Points and sets. Axioms on sets. Subsets. Operations on sets.

Foundations, II: Functions (3–4 weeks)

Ordered pairs. Relations, functions, and operations. Injections, surjections, and bijections. Binary operations and their properties.

A Deeper Look at the Real Numbers (3–4 weeks)

The integers. Algebraic and order properties. Completeness. Supremum Property. Intervals, decimals, and rational and irrational numbers. Mathematical induction. The Archimedean Property. Recursion. Primes. Finiteness and infinity. Countability and uncountability.

Equivalence Relations (2 weeks)

Reflexivity, symmetry, and transitivity. The Equivalence-Relation Theorem. Elementary functions.

Type
Chapter
Information
The Moore Method
A Pathway to Learner-Centered Instruction
 , pp. 211 - 216
Publisher: Mathematical Association of America
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×