How to Think Like a Mathematician : A Companion to Undergraduate Mathematics

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician. This Arsenal Of Tips And Techniques Eases New Students Into Undergraduate Mathematics, Unlocking The World Of Definitions, Theorems, And Proofs. I. Study Skills For Mathematicians -- Ii. How To Think Logically -- Iii. Definitions, Theorems And Proofs -- Iv. Techniques Of Proof -- V. Mathematics That All Good Mathematicians Need -- Vi. Closing Remarks. Kevin Houston. Includes Index. Includes Bibliographical References And Index. Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; PART I Study skills for mathematicians; PART II How to think logically; PART III Definitions, theorems and proofs; PART IV Techniques of proof; PART V Mathematics that all good mathematicians need; PART VI Closing remarks; APPENDIX A Greek alphabet; APPENDIX B Commonly used symbols and notation; APPENDIX C How to prove that ... ; Index. Looking for a head start in your undergraduate degree in mathematics? This friendly companion eases beginning students into real mathematical thinking, unlocking important techniques for effective mathematics so you can communicate with clarity, solve problems, and explore the world of definitions, theorems and proofs with real confidence. Publisher Description (unedited publisher data) This arsenal of tips and techniques eases new students into undergraduate mathematics, unlocking the world of definitions, theorems, and proofs