Introduction To Mathematical Proofs: A Transiti...

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3 hours; 3 creditsAn introduction to mathematical proofs and a transition to advanced mathematics. Elements of mathematical language: basic set theory and logic. Direct proof, proof by contrapositive and proof by contradiction. Counterexample and disproof. Relations. Functions. Mathematical induction. Countable and uncountable sets. Proofs in elementary number theory. Development of the real numbers. Properties of the real number system: order, uncountability, completeness, least upper bound property, and the existence of the limits of Cauchy sequences.Corequisite: Mathematics *1206

Course: MATH-UA 125 Introduction to Mathematical Proofs/ MTHED-UE 1049 Mathematical Proof and ProvingCourse Description: This course introduces elements of mathematical proof, focusing on three mains themes: 1. The meaning of mathematical statements -- universal/existential; 2. The role of examples in determining the validity of mathematical statements; 3. The various forms and methods of mathematical proofs, including direct (deductive) proof; proof by exhaustion; indirect proof (by contradiction, or by contrapositive); mathematical induction; and disproof by counterexample. This is a problem-based course. Lessons are structured around activities that engage students in doing proofs that are meaningful to them and based on mathematical topics with which they are familiar.Syllabus: pdf Instructors: Jalal Shatah and Orit Zaslavsky, shatah(at-sign)cims.nyu.edu, oz2(at-sign)nyu.eduMeeting Time/Location: Monday 1145AM-2PM, (formerly KIMM 804) changed to WWH 317TA: Steven Heilman, heilman(at-sign)cims.nyu.eduTA Office Hours: WWH 1108, Thursday, 11AM-1PM, or by appointment (If this time is bad for many people, let me know and I will make a change.)Recommended Textbooks: Chartrand, Polimeni and Zhang, Mathematical Proofs: A Transition to Advanced Mathematics. Fendel and Resek, Foundations of Higher Mathematics: Exploration and Proof.Other Resources: An introduction to mathematical arguments, Michael Hutchings An Introduction to Mathematical Proofs, Jimmy Arnold.ch1ch2ch3ch4ch5

Course Description: An introduction to proof in mathematics: logic, sets, relations, functions and cardinality, a first look at epsilon-delta methods of proof. Writing and communication of mathematical ideas will be emphasized

Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity. They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs.

Ping Zhang is Professor of Mathematics at Western Michigan University. She received her Ph.D. in mathematics from Michigan State University. Her research is in the area of graph theory and algebraic combinatorics. Professor Zhang has authored or co-authored more than 200 research papers and four textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. She serves as an editor for a series of books on special topics in mathematics. She has supervised 7 doctoral students and has taught a wide variety of undergraduate and graduate mathematics courses including courses on introduction to research. She has given over 60 lectures at regional, national and international conferences. She is a council member of the Institute of Combinatorics and Its Applications and a member of the American Mathematical Society and the Association of Women in Mathematics.

Thus, the purpose of Prove it! Math Academy is to provide an introduction to mathematical proof in a creative, problem-solving context. Our summer program accomplishes this in a safe, scenic, memorable location, surrounded by like-minded peers and outstanding instructors, so that our students can reach their full potential.

This book is intended to be used for a one-semester/quarter introduction to proof course (sometimes referred to as a transition to proof course). The purpose of this book is to introduce the reader to the process of constructing and writing formal and rigorous mathematical proofs. The intended audience is mathematics majors and minors. However, this book is also appropriate for anyone curious about mathematics and writing proofs. Most users of this book will have taken at least one semester of calculus, although other than some familiarity with a few standard functions in Chapter 8, content knowledge of calculus is not required. The book includes more content than one can expect to cover in a single semester/quarter. This allows the instructor/reader to pick and choose the sections that suit their needs and desires. Each chapter takes a focused approach to the included topics, but also includes many gentle exercises aimed at developing intuition. 781b155fdc