Description: About this productSynopsisAims to bridge the gap between calculus and advanced math. This book guides students to think precisely and to express themselves mathematically to analyze a situation, extract pertinent facts, and draw appropriate conclusions. It also helps to improve the student's ability to think and write in a mature mathematical fashion.TRANSITION TO ADVANCED MATHEMATICS bridges the gap between calculus and advanced math in at least three ways. First, it guides students to think precisely and to express themselves mathematically-to analyze a situation, extract pertinent facts, and draw appropriate conclusions. Second, it provides a firm foundation of the basic concepts and methods needed for continued work. Finally, it provides introductions to concepts of modern algebra and analysis in sufficient depth to capture some of their spirit and characteristics. The text will improve the student's ability to think and write in a mature mathematical fashion and provide a solid understanding of the material most useful for advanced courses.Product IdentifiersISBN-100534399002ISBN-139780534399009eBay Product ID (ePID)46021159Key DetailsAuthorDouglas Smith, Maurice Eggen, Richard St AndreNumber Of Pages384 pagesFormatHardcoverPublication Date2005-06-14LanguageEnglishPublisherBrooks/ColePublication Year2005Additional DetailsEdition Number6Copyright Date2006IllustratedYesDimensionsWeight26.5 OzHeight0.8 In.Width7.3 In.Length9.2 In.Target AudienceGroupCollege AudienceClassification MethodLCCN2005-922091LC Classification NumberQA37.3.S65 2006Dewey Decimal510Dewey Edition23Table Of Content1. 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 (optional). 2. 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 (optional). 3. RELATIONS. Cartesian Products and Relations. Equivalence Relations. Partitions. Ordering Relations (optional). Graphs of Relations (optional). 4. FUNCTIONS. Functions as Relations. Constructions of Functions. Functions That Are Onto; One-to-One Functions. Induced Set Functions. Sequences as Functions (optional). 5. CARDINALITY. Equivalent Sets; Finite Sets. Infinite Sets. Countable Sets. The Ordering of Cardinal Numbers. Comparability of Cardinal Numbers and the Axiom of Choice (optional). 6. CONCEPTS OF ALGEBRA: GROUPS (optional). Algebraic Structures. Groups. Examples of Groups. Subgroups. 7. CONCEPTS OF ANALYSIS: COMPLETENESS OF THE REAL NUMBERS (optional). Ordered Field Properties of the Real Numbers. The Heine-Borel Theorem. The Bolzano-Weierstrass Theorem. The Bounded Monotone Sequence Theorem. Equivalents of Completeness. Answers to Exercises. Index. List of Symbols.
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Number of Pages: 384 Pages
Publication Name: Transition to Advanced Mathematics
Language: English
Publisher: Brooks/Cole
Subject: General, Algebra / Elementary
Publication Year: 2005
Item Height: 0.8 in
Item Weight: 26.5 Oz
Type: Textbook
Subject Area: Mathematics
Item Length: 9.2 in
Author: Douglas Smith, Richard St Andre, Maurice Eggen
Item Width: 7.3 in
Format: Hardcover
