Bridge to Abstract Mathematics
Home > Mathematics and Science Textbooks > Mathematics > Mathematical foundations > Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)
Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)

Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

Mathematics is a science that concerns theorems that must be proved within a system of axioms and definitions. With this book, the mathematical novice will learn how to prove theorems and explore the universe of abstract mathematics. The introductory chapters familiarise the reader with some fundamental ideas, including the axiomatic method, symbolic logic and mathematical language. This leads to a discussion of the nature of proof, along with various methods for proving statements. The subsequent chapters present some foundational topics in pure mathematics, including detailed introductions to set theory, number systems and calculus. Through these fascinating topics, supplemented by plenty of examples and exercises, the reader will hone their proof skills. This complete guide to proof is ideal preparation for a university course in pure mathematics, and a valuable resource for educators.

Table of Contents:
Some notes on notation; To the students; For the professors; Part I. The Axiomatic Method: 1. Introduction; 2. Statements in mathematics; 3. Proofs in mathematics; Part II. Set Theory: 4. Basic set operations; 5. Functions; 6. Relations on a set; 7. Cardinality; Part III. Number Systems: 8. Algebra of number systems; 9. The natural numbers; 10. The integers; 11. The rational numbers; 12. The real numbers; 13. Cantor's reals; 14. The complex numbers; Part IV. Time Scales: 15. Time scales; 16. The Delta Derivative; Part V. Hints: 17. Hints for (and comments on) the exercises; Index.

About the Author :
Ralph W. Oberste-Vorth earned his PhD in mathematics from Cornell University. In 2002, he became the Chairman of the Department of Mathematics at Marshall University. In 2011, he accepted a position as the Chairman of the Department of Mathematics and Computer Science at Indiana State University. Aristides Mouzakitis received his BA and MA in mathematics from Hunter College. In Greece, he has worked as a teacher in secondary education and as an English-Greek translator of popular mathematics books and articles. In 2009, he earned his doctorate in mathematics education from the University of Exeter. Bonita Lawrence is a Professor of Mathematics at Marshall University. She received her baccalaureate degree in mathematics education from Cameron University in 1979. After ten years of teaching, she returned to school and earned her Master's degree in mathematics at Auburn University and went on to receive her PhD in mathematics from the University of Texas, Arlington.

Review :
For a variety of reasons, over the past 30 years or so, ""bridge"" or ""transition"" courses have become staples in the undergraduate mathematics curriculum. The purpose of these courses, broadly speaking, is to introduce students to abstract and rigorous mathematical thinking, at a level appropriate to their learning, to make conjectures and construct proofs--things they do not usually see in calculus at present. This work by Oberste-Vorth (Indiana State), Mouzakitis (Second Junior High School of Corfu, Greece), and Lawrence (Marshall Univ.) has evolved from courses taught at the University of South Florida and Marshall University and is worthy of consideration. Coverage includes standard ideas involving set, functions, relations, and cardinality as well as mathematical statements and logic and types of proof. Building on these early notions, an instructor can then choose to go in the direction of number systems (including construction of the reals from the rationals) with an algebraic flavor or toward analysis (here, including time scales and continuity). The analysis direction is perhaps the rockier road to travel. Given the purpose and the audience, the exposition is commendably open and not terse. The book includes scores of exercises scattered throughout, with many end-of-chapter supplemental exercises."" - D. Robbins, CHOICE ""To begin the process of being able to write and understand proofs it is necessary for the student to go back a few squares on the mathematical board game and learn the rigorous definitions of concepts such as the structure of mathematical statements, set theory and the underlying structural definitions of the basic number systems. Knowing these concepts very well gives the student the foundation for entering the proof realm and it helps to overturn their complacent belief of understanding. This book is designed to give the reader that understanding and the mission is a success. The authors provide detailed explanations of the foundations of mathematics needed to work comfortably with proofs, both operationally and theoretically. It would be an excellent choice for a freshman/sophomore level course in the foundations of mathematics designed to prepare students for the rigors of proofs that they will experience in their later years."" - Charles Ashbacher, Journal of Recreational Mathematics


Best Sellers


Product Details
  • ISBN-13: 9780883857793
  • Publisher: Mathematical Association of America
  • Publisher Imprint: Mathematical Association of America
  • Height: 260 mm
  • No of Pages: 249
  • Series Title: Mathematical Association of America Textbooks
  • Weight: 590 gr
  • ISBN-10: 0883857790
  • Publisher Date: 24 Jan 2013
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Spine Width: 20 mm
  • Width: 182 mm


Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)
Mathematical Association of America -
Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Bridge to Abstract Mathematics: (Mathematical Association of America Textbooks)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    New Arrivals


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!