This is a textbook for an undergraduate Mathematics major transition course from technique-based Mathematics (such as Algebra and Calculus) to proof-based mathematics.
A topologist, he has published 35 peer-reviewed research papers, and the book Convergence Foundations of Topology , revisiting classical General Topology from the point of view of his area of research: convergence spaces..
Originally from France where he obtained his PhD in 1999, he has been teaching at various universities in the US since 2001, teaching a wide spectrum of Mathematics courses, from entry level to graduate courses.
About the Author Fr d ric Mynard is currently a professor of Mathematics at New Jersey City University.
The primary audience is undergraduate Mathematics major, but independent readers interested in Mathematics can also use the book for self-study.
An appendix gives some complement on induction and order, and another provides full solutions of the in-text exercises.
The last chapter treats infinite cardinalities.
An in-depth treatment of relations, particularly equivalence and order relations completes the exposition of the basic Language of mathematics.
It then moves to a discussion of proof structure and basic proof techniques, including proofs by induction with extensive examples.
It motivates the Introduction of the formal Language of logic and set theory and develops the basics with examples, exercises with solutions and exercises without.
This is a textbook for an undergraduate Mathematics major transition course from technique-based Mathematics (such as Algebra and Calculus) to proof-based mathematics
