عنوان

Book of Proof

(Number (ISBN

9780989472104

Number

dltt

Title Proper

Book of Proof

General Material Designation

[Book]

First Statement of Responsibility

Richard Hammack

Specific Material Designation and Extent of Item

1 online resource

Series Title

Open textbook library

Frequency

Updated irregularly

Text of Note

I Fundamentals -- 1. Sets -- 2. Logic -- 3. Counting -- II How to Prove Conditional Statements -- 4. Direct Proof -- 5. Contrapositive Proof -- 6. Proof by Contradiction -- III More on Proof -- 7. Proving Non-Conditional Statements -- 8. Proofs Involving Sets -- 9. Disproof -- 10. Mathematical Induction -- IV Relations, Functions and Cardinality -- 11. Relations -- 12. Functions -- 13. Cardinality of Sets

0

Text of Note

This is a book about how to prove theorems. Until this point in your education, you may have regarded mathematics primarily as a computational discipline. You have learned to solveequations, compute derivatives and integrals, multiply matrices and finddeterminants; and you have seen how these things can answer practicalquestions about the real world. In this setting, your primary goal in usingmathematics has been to compute answers. But there is another approach to mathematics that is more theoreticalthan computational. In this approach, the primary goal is to understandmathematical structures, to prove mathematical statements, and evento invent or discover new mathematical theorems and theories. Themathematical techniques and procedures that you have learned and usedup until now have their origins in this theoretical side of mathematics. Forexample, in computing the area under a curve, you use the fundamentaltheorem of calculus. It is because this theorem is true that your answeris correct. However, in your calculus class you were probably far moreconcerned with how that theorem could be applied than in understandingwhy it is true. But how do we know it is true? How can we convinceourselves or others of its validity? Questions of this nature belong to thetheoretical realm of mathematics. This book is an introduction to that realm. This book will initiate you into an esoteric world. You will learn andapply the methods of thought that mathematicians use to verify theorems,explore mathematical truth and create new mathematical theories. Thiswill prepare you for advanced mathematics courses, for you will be betterable to understand proofs, write your own proofs and think critically andinquisitively about mathematics. This text has been used in classes at:Virginia Commonwealth University, Lebanon Valley College, University of California - San Diego, Colorado State University, Westminster College, South Dakota State University, PTEK College - Brunei, Christian Brothers High School, University of Texas Pan American, Schola Europaea, James Madison University, Heriot-Watt University, Prince of Songkla University, Queen Mary University of London, University of Nevada - Reno, University of Georgia - Athens, Saint Peter's University, California State University,Bogaziçi University, Pennsylvania State University, University of Notre Dame

Mathematics, Textbooks

Hammack, Richard

Hammack, Richard

Open Textbook Library, distributor

Date of Transaction

20190502180339.0

Electronic name

[Book]

Y