Mathematical Proofs: A Transition to Advanced Mathematics
- Downloads：5932
- Type：Epub+TxT+PDF+Mobi
- Create Date：2022-09-12 07:55:28
- Update Date：2025-09-06
- Status：finish
- Author：Gary Chartrand
- ISBN：1292040645
- Environment：PC/Android/iPhone/iPad/Kindle
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Summary
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。
Reviews
Nasir Ali
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Don't usually rate/review textbooks but I couldn't let this one slide。 To begin things， the book surely lives upto what it promises by providing a complete， comprehensive and swift introduction to everything it covers。 It begins with Sets and Logics， and proceeds all the way to abstract algebra， covering alot of ground but while maintaining it's quality throughout， giving one the unfiltered essence of pure mathematics。 As a Physics Major， one would routinely encounter numerous math subjects but Don't usually rate/review textbooks but I couldn't let this one slide。 To begin things， the book surely lives upto what it promises by providing a complete， comprehensive and swift introduction to everything it covers。 It begins with Sets and Logics， and proceeds all the way to abstract algebra， covering alot of ground but while maintaining it's quality throughout， giving one the unfiltered essence of pure mathematics。 As a Physics Major， one would routinely encounter numerous math subjects but whenever I find a textbook and try to go through them， I commonly get lost in mathematical literature， rigorous notations and the author always assuming you know more than you would while leaving major theorems and lemmas as an exercise for the reader。 The book provides solutions to all these problems， as for the proofs themselves， I rarely felt like referring to another source or googling the matter hand， as any proof out of the ordinary would either have a section of 'proof strategy' before the formal one or contain a 'proof analysis' afterwards。 All in all， an engaging and fruitful book， would recommend to anyone （with a little background to basic math and single variable calculus） willing to dive deeper into advanced mathematics。 。。。more
Yannick
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It is sooo good。 Self-studying pure mathematics is a hard undertaking。 Anyone who ever tried knows that。 This book makes it easier than any university course I have ever taken。 Working carefully and slowly through this book， doing all exercises and afterwards checking the solutions manual， honestly feels like having a really good teacher。 I recommend 4th edition though。 It includes chapters for intermediate and fairly advanced topics like group theory， ring theory， metric spaces， topology， real It is sooo good。 Self-studying pure mathematics is a hard undertaking。 Anyone who ever tried knows that。 This book makes it easier than any university course I have ever taken。 Working carefully and slowly through this book， doing all exercises and afterwards checking the solutions manual， honestly feels like having a really good teacher。 I recommend 4th edition though。 It includes chapters for intermediate and fairly advanced topics like group theory， ring theory， metric spaces， topology， real analysis， linear algebra etc。 。。。more
Patrick Lu 派派
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Topology proofs looking real tasty。
Dayton Outar
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I think this is an excellent book。The proofs are brief and straight to the point。 Sometimes， I had to find a few YouTube videos to help me grasp the concepts。 But very good material and it will prove to be useful to make reference to when reading other Mathematics books。
Beth G
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This is a really nice text。 It's written in an accessible and student-friendly style that doesn't sacrifice content or clarity。 Highly recommended to anyone looking to build a strong foundation for proofs！ This is a really nice text。 It's written in an accessible and student-friendly style that doesn't sacrifice content or clarity。 Highly recommended to anyone looking to build a strong foundation for proofs！ 。。。more
Pranjal Singh
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While I have done an undergraduate course on proofs （HUL251 Intro to logic @ IIT Delhi）， this book was a really helpful book for theory i。e。 elements of mathematical proof （sets， relations， induction， contradiction， truth tables etc。） and practice i。e。 the last half of the book on proofs in different branches of mathematics。 Helped me a lot in beginning of a course on Numerical Linear Algebra。
Justin Ritter
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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！
Guy
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Muuuch better than Girls & Sex: Navigating the Complicated New Landscape！！ Muuuch better than Girls & Sex: Navigating the Complicated New Landscape！！ 。。。more
Thomas Bell
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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。 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。 。。。more
Vincent Manapat
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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。 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。 。。。more
CR
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