9780495562023

A Transition to Advanced Mathematics

by ; ;
  • ISBN13:

    9780495562023

  • ISBN10:

    0495562025

  • Edition: 7th
  • Format: Hardcover
  • Copyright: 6/1/2010
  • Publisher: Brooks Cole
  • View Upgraded Edition

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping On Orders Over $59!
    Your order must be $59 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • Get Rewarded for Ordering Your Textbooks! Enroll Now
  • Complimentary 7-Day eTextbook Access - Read more
    When you rent or buy this book, you will receive complimentary 7-day online access to the eTextbook version from your PC, Mac, tablet, or smartphone. Feature not included on Marketplace Items.
  • eCampus.com Device Compatibility Matrix

    Click the device icon to install or view instructions

    Apple iOS | iPad, iPhone, iPod
    Android Devices | Android Tables & Phones OS 2.2 or higher | *Kindle Fire
    Windows 8 / 7 / Vista / XP
    Mac OS X | **iMac / Macbook
    Enjoy offline reading with these devices
    Apple Devices
    Android Devices
    Windows Devices
    Mac Devices
    iPad, iPhone, iPod
    Our reader is compatible
     
     
     
    Android 2.2 +
     
    Our reader is compatible
     
     
    Kindle Fire
     
    Our reader is compatible
     
     
    Windows
    8 / 7 / Vista / XP
     
     
    Our reader is compatible
     
    Mac
     
     
     
    Our reader is compatible

Supplemental Materials

What is included with this book?

  • The Used and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Summary

A TRANSITION TO ADVANCED MATHEMATICS helps students make the transition from calculus to more proofs-oriented mathematical study. The most successful book of its kind, the 7th edition continues to provide a firm foundation in major concepts needed for continued study and guides users to think and express themselves mathematically—to analyze a situation, extract pertinent facts, and draw appropriate conclusions. The authors place continuous emphasis throughout on improving users' ability to read and write proofs, and on developing their critical awareness for spotting common errors in proofs. Concepts are clearly explained and supported with detailed examples, while abundant and diverse exercises provide thorough practice on both routine and more challenging problems. Students will come away with a solid intuition for the types of mathematical reasoning they'll need to apply in later courses and a better understanding of how mathematicians of all kinds approach and solve problems.

Table of Contents

Logic And Proofs
Propositions and Connectives
Conditionals and Biconditionals
Quantifiers
Basic Proof Methods I
Basic Proof Methods II
Proofs Involving Quantifiers
Additional Examples of Proofs
Set Theory
Basic Notions of Set Theory
Set Operations
Extended Set Operations and Indexed Families of Sets
Induction
Equivalent Forms of Induction
Principles of Counting
Relations And Partitions
Relations
Equivalence Relations
Partitions
Ordering Relations
Graphs
Functions
Functions as Relations
Constructions of Functions
Functions That Are Onto
One-to-One Functions
One-to-One Correspondences and Inverse Functions
Images of Sets.
Sequences
Cardinality
Equivalent Sets
Finite Sets
Infinite Sets
Countable Sets
The Ordering of Cardinal Numbers
Comparability of Cardinal Numbers and the Axiom of Choice
Concepts Of Algebra: Groups
Algebraic Structures
Groups
Subgroups
Operation Preserving Maps
Rings and Fields
Concepts Of Analysis: Completeness Of The Real Numbers
Ordered Field Properties of the Real Numbers
The Heine-Borel Theorem
The Bolzano-Weierstrass Theorem
The Bounded Monotone Sequence Theorem
Comparability of Cardinals and the Axiom of Choice
Table of Contents provided by Publisher. All Rights Reserved.

Rewards Program

Write a Review