Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Proofs and Fundamentals

A First Course in Abstract Mathematics

  • Textbook
  • © 2003

Overview

Authors:
  1. Ethan D. Bloch

    1. Department of Mathematics and Computer Science, Bard College, Annandale-on-Hudson, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. Proofs

    1. Front Matter

      Pages 1-1
      Download chapter PDF

    2. Informal Logic

      • Ethan D. Bloch
      Pages 3-54

    3. Strategies for Proofs

      • Ethan D. Bloch
      Pages 55-103

  3. Fundamentals

    1. Front Matter

      Pages 105-105
      Download chapter PDF

    2. Sets

      • Ethan D. Bloch
      Pages 107-133

    3. Functions

      • Ethan D. Bloch
      Pages 135-176

    4. Relations

      • Ethan D. Bloch
      Pages 177-201

    5. Infinite and Finite Sets

      • Ethan D. Bloch
      Pages 203-248

  4. Extras

    1. Front Matter

      Pages 249-249
      Download chapter PDF

    2. Selected Topics

      • Ethan D. Bloch
      Pages 251-321

    3. Number Systems

      • Ethan D. Bloch
      Pages 323-362

    4. Explorations

      • Ethan D. Bloch
      Pages 363-373

  5. Back Matter

    Pages 375-424
    Download chapter PDF
Back to top

Keywords

About this book

In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for­ mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces­ sively pedagogical, and too full to distractions. Some of features of this text are the following: (1) Symbolic logic and the use of logical notation are kept to a minimum. We discuss only what is absolutely necessary - as is the case in most advanced mathematics courses that are not focused on logic per se.

Reviews

". . . Proofs and Fundamentals has many strengths. One notable, strength, is its excellent organization. The book begins with a three-part preface, which makes its aims very clear. There are large exercise sets throughout the book . . . Exercises are well integrated with the text and vary appropriately from easy to hard . . . Topics in Part III are quite varied, mostly independent from each other, and truly dependent on Parts I and II. At the end of the book there are useful hints to selected exercises.

Perhaps the book’s greatest strength is the author’s zeal and skill for helping students write mathematics better. Careful guidance is given throughout the book. Basic issues like not abusing equal signs are treated explicitly. Attention is given to even relatively small issues, like not placing a mathematical symbol directly after a punctuation mark. Throughout the book, theorems are often followed first by informative ‘scratch work’ and only then by proofs. Thus students can see many examples of what they should think, what they should write, and how these are usually not the same."

–MAA Online

"This is a well-written book, based on very sound pedagogical ideas. It would be an excellent choice as a textbook for a 'transition' course." ---Zentralblatt Math

Authors and Affiliations

  • Department of Mathematics and Computer Science, Bard College, Annandale-on-Hudson, USA

    Ethan D. Bloch

Bibliographic Information

  • Book Title: Proofs and Fundamentals

  • Book Subtitle: A First Course in Abstract Mathematics

  • Authors: Ethan D. Bloch

  • DOI: https://doi.org/10.1007/978-1-4612-2130-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2003

  • eBook ISBN: 978-1-4612-2130-2Published: 01 December 2013

  • Edition Number: 1

  • Number of Pages: XXI, 424

  • Topics: Mathematical Logic and Foundations, Mathematics, general

Publish with us

Policies and ethics

Back to top

Search

Navigation