Mathematical foundations Books

Book SynopsisStep right up! Come take part in the county fair, where you’ll see fractions, decimals, and percents everywhere. Gobble up a fraction of pie, boost your batting average in the arcade, and take a percent off the price of a toy. Learning about equivalent parts equals a whole lot of fun in this straightforward introduction to a challenging concept.

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Book Synopsis-Preface.-1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (Bbb R).- 14. Functions, Domain, and Range.-15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat's Little Theorem.- 29. Projects.- Appendix.- References.- Index.Trade ReviewFrom the reviews of the second edition:“The book is written in an informal way, which could please the beginners and not offend the more experienced reader. A reader can find a lot of problems for independent study as well as a lot of illustrations encouraging him/her to draw pictures as an important part of the process of mathematical thinking.”—European Mathematical Society, September 2011"Several areas like sets, functions, sequences and convergence are dealt with and several exercises and projects are provided for deepening the understanding. …It is the impression of the author of this review that the book can be particularly strongly recommended for teacher students to enable them to catch and transfer the “essence” of mathematical thinking to their pupils. But also everybody else interested in mathematics will enjoy this very well written book.—Burkhard Alpers (Aalen), zbMATH“The book is primarily concerned with an exposition of those parts of mathematics in which students need a more thorough grounding before they can work successfully in upper-division undergraduate courses. … a mathematically-conventional but pedagogically-innovative take on transition courses.” —Allen Stenger, The Mathematical Association of America, September, 2011Table of Contents-Preface. -1. The How, When, and Why of Mathematics.- 2. Logically Speaking.- 3.Introducing the Contrapositive and Converse.- 4. Set Notation and Quantifiers.- 5. Proof Techniques.- 6. Sets.- 7. Operations on Sets.- 8. More on Operations on Sets.- 9. The Power Set and the Cartesian Product.- 10. Relations.- 11. Partitions.- 12. Order in the Reals.- 13. Consequences of the Completeness of (\Bbb R).- 14. Functions, Domain, and Range.- 15. Functions, One-to-One, and Onto.- 16. Inverses.- 17. Images and Inverse Images.- 18. Mathematical Induction.- 19. Sequences.- 20. Convergence of Sequences of Real Numbers.- 21. Equivalent Sets.- 22. Finite Sets and an Infinite Set.- 23. Countable and Uncountable Sets.- 24. The Cantor-Schröder-Bernstein Theorem.- 25. Metric Spaces.- 26. Getting to Know Open and Closed Sets.- 27. Modular Arithmetic.- 28. Fermat’s Little Theorem.- 29. Projects.- Appendix.- References.- Index.

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Book SynopsisWhen Are We Ever Going to Use This Stuff? College Mathematics for the Liberal Arts Major is a college level mathematics textbook designed with liberal arts majors in mind. This text uses practical, entertaining topics presented in a readable, student-centered style to teach mathematics concepts and skills for the non-STEM major.While emphasizing practical application over symbolic manipulation, students learn where, when, why, and how the math they learn will help them in their lives. Specific topics include consumer math, apportionment, statistics, probability, set theory, geometry, right triangle trigonometry, and voting techniques, with the history of mathematics as a consistent motivational thread throughout. Concepts are taught within familiar contexts with a focus on the development of problem-solving skills.The eighth edition features a few new historical topics and additional readings in each chapter, updated examples to make the material more relevant, and "From a Different Point of View" sections throughout to emphasize alternative perspectives. To help students and teachers cope with the emerging national trend of reducing or eliminating prerequisite courses, a significant number of review passages have been woven throughout the material.Trade ReviewStudent reviews for the book and Active Learning components:"We actually learn how to apply this math, when this math will be applied, and why it is used in real life. Therefore, instead of just memorizing formulas we actually know what each variable in a formula means and why it is arranged a certain way.""The book is written in an easy to understand language and is filled with helpful examples. As someone who is not very good at math, having so many opportunities to practice examples really helped me understand the material." "This is the best textbook I've ever used. I appreciated the easy and informal language used to explain things in a way that was very easy to understand. Teaches you about concepts related to life.""The instructional videos were an awesome way to learn. As a visual learner, I enjoyed the ability to go back and re-watch the videos if I felt like I wasn't grasping the concept of a particular item well enough.""The textbook is clearly written and helpful, the online exercises reinforce what's learned, and it's presented in a way that makes it accessible and applicable to the 'real world.' I learned something from EVERY exercise in this class.""The study tools definitely made a difference for me. I am a hands-on learner, so I was initially worried about taking online classes but the videos, PowerPoints, and games gave better understanding to me after I read the book." "The videos were great. The book helped reinforce all the information and the games were really fun and a great learning tool.""I really liked the Check Yourself games! Those were extremely helpful and fun in practicing different math problems.""The interactive games actually make the math easy to learn.""The book was amazing in that all the material was so easy to understand. It's as if they took a survey of all the things people wished were different about their previous math books and applied them to this book.""The video lessons were clearly explained and made the material accessible. Having review games available before each quiz provided a good way to review relevant information and let me know what sort of things to expect on the quizzes.""Math is a tough subject for me, and I found all of the learning material to be extremely useful in my learning process.

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Book Synopsis

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