Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. K Mathematical Proofs: A Transition to Advanced Mathematics, 2/e, prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets. KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory. MARKET: For all readers interested in advanced mathematics and logic....
|Title||:||Mathematical Proofs: A Transition to Advanced Mathematics|
|Number of Pages||:||384 Pages|
|Status||:||Available For Download|
|Last checked||:||21 Minutes ago!|
Mathematical Proofs: A Transition to Advanced Mathematics Reviews
This is the book I should have been given for my introduction to theoretical math. Instead, I was taught to mechanically handle epsilon-delta proofs and struggled with proofs in later classes. This book provides a great number of concise but rigorous proofs that build confidence for tackling future subjects. Great read!
Clear and accessible text for any one has a little background in mathematics ( basic algebra skills, some background in single variable calculus is preferred but not necessary).In my opinion it might be the best starting point to get into advanced pure mathematics.The whole book can be divided into 4 main parts :1- Introduction to simple logic and set theory.2- Methods of proofs in Mathematics ( Trivial & Vacuous proofs, Direct proofs, Proofs by contrapositive, by contradiction, by a counter example, by induction and the least element principle ), with many in-text exercises.3- Equivalence Relations, functions and cardinalities of sets.This part consists of three chapters and its the hardest, and important for any future investigation in pure mathematics.4- Applications of proof techniques in different mathematical fields ( Number theory, Calculus, Group theory, Ring Theory, Linear Algebra and Topology )Note : The last three chapters are not included in the book, but available online on :http://wps.aw.com/aw_chartrand_mathpr...
Definitely one of the better Pearson text books ive read. Readin Pearson texts books is usually like standing in line at a government office. Mathematical Proofs really is a transition to advanced math, and I will definitely feel more complete studying advanced level calculus after reading this text. It offers a nice intro to set theory and logic that leads up to the basics of proving, and finishes off with the theoretically important proofs that found calculus, number theory and group theory.
Clear, precise, and altogether excellent introduction of proofs and basic set theory. I'm glad historical context and facts about the development of logic were given (a move few maths textbooks have the balls to do). If you're looking to get into real maths, not the BS taught up to college, this is a great starting point.
I can't say enough good things about this textbooks -- it's definitely one of the best I have ever used. It's small and extremely concise and not burdened by tons of graphics and sidebars and sidenotes. Just exactly what you need to know, broken down into small pieces.
Muuuch better than Girls & Sex: Navigating the Complicated New Landscape!!
Yay! Finally finished reading this book - and teaching it to my students. I really liked it actually, and yes, although I didn't teach sections 12.5 or 12.6 or chapter 13, I did actually read those as well. :-)This book is not for everyone. At all. Just letting you know.