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Set Theory for Beginners: A Rigorous Introduction to Sets, Relations, Partitions, Functions, Induction, Ordinals, Cardinals, Martin’s Axiom, and Stationary Sets
Set Theory for BeginnersSet Theory for Beginners consists of a series of basic to intermediate lessons in set theory. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for
professors teaching an undergraduate course or basic graduate course in set theoryhigh school teachers working with advanced math studentsstudents wishing to see the type of mathematics they would be exposed to as a math major.The material in this pure math book lessons consisting of basic to intermediate topics in set theory and mathematical logic.A problem set after each lesson arranged by difficulty level.A complete solution guide is included as a downloadable PDF file.Set Theory Book Table Of Contents (Selected) Here's a selection from the table of Lesson 1 - SetsLesson 2 - SubsetsLesson 3 - Operations on SetsLesson 4 - RelationsLesson 5 - Equivalence Relations and PartitionsLesson 6 - FunctionsLesson 7 - EquinumerosityLesson 8 - Induction and Recursion on NLesson 9 - Propositional LogicLesson 10 - First-order LogicLesson 11 - Axiomatic Set TheoryLesson 12 - OrdinalsLesson 13 - CardinalsLesson 14 - Martin's AxiomLesson 15 - The Field of Real NumbersLesson 16 - Clubs and Stationary Sets
professors teaching an undergraduate course or basic graduate course in set theoryhigh school teachers working with advanced math studentsstudents wishing to see the type of mathematics they would be exposed to as a math major.The material in this pure math book lessons consisting of basic to intermediate topics in set theory and mathematical logic.A problem set after each lesson arranged by difficulty level.A complete solution guide is included as a downloadable PDF file.Set Theory Book Table Of Contents (Selected) Here's a selection from the table of Lesson 1 - SetsLesson 2 - SubsetsLesson 3 - Operations on SetsLesson 4 - RelationsLesson 5 - Equivalence Relations and PartitionsLesson 6 - FunctionsLesson 7 - EquinumerosityLesson 8 - Induction and Recursion on NLesson 9 - Propositional LogicLesson 10 - First-order LogicLesson 11 - Axiomatic Set TheoryLesson 12 - OrdinalsLesson 13 - CardinalsLesson 14 - Martin's AxiomLesson 15 - The Field of Real NumbersLesson 16 - Clubs and Stationary Sets
208 pages, Kindle Edition
Published February 20, 2019
5 people are currently reading
15 people want to read
About the author
Steve Warner
110 books9 followersDr. Steve Warner is a mathematician and test prep expert who has been tutoring students in mathematics for standardized tests since 1999. During this time Dr. Warner has used the feedback from thousands of students to develop a unique system that can be used by anyone to drastically improve his or her math score in a very short period of time.
Dr. Warner's philosophy is quite different from most experts in that he focuses on test-specific strategy designed to save time, avoid carelessness, and exploit the weaknesses of standardized tests, as opposed to spending valuable time on the conventional teaching of mathematics. Furthermore, Dr. Warner realizes that students at different score levels must be taught differently and this is reflected very strongly in his materials.
Dr. Warner began tutoring his classmates while he was still in high school, and by the time he started college he had already tutored over 100 students in subjects ranging from algebra to AP calculus. He soon became known as the "math ninja" because of his incredible ability to help students get over a 90 on their tests with just one short tutoring session.
Throughout college Dr. Warner began tutoring more advanced topics such as linear algebra, differential equations and advanced calculus. His ability to get even the weakest math majors to understand deep theoretical concepts became well known throughout the campus. During this time he received several math scholarships and a 4.0 in mathematics, but it wasn't until graduate school that Dr. Warner had an experience which changed his philosophy on teaching forever....
When Dr. Warner began graduate school he actually found himself struggling with the material for the first time. He worked harder than he ever had in the past, but was not able to grasp the concepts as easily as he had as an undergraduate. Dr. Warner finally experienced the feelings that his clients went through. But an interesting thing happened soon after. All of a sudden nothing seemed difficult anymore and he was back at the top of his class. Despite the fact that he was taking even harder classes now, he was once again breezing through them with very little effort.
It was at this time that Dr. Warner had two realizations.
(1) Working harder and long hours does not necessarily lead to more success in mathematics.
(2) It is possible for anyone to increase their skill in mathematics to any level they choose.
You see, during that first year Dr. Warner experimented with many methods to get himself to learn material that was too difficult for him. And eventually he figured it out. It was this final step in his evolution that allowed him to become an even more effective tutor than ever before. What he learned during this process was incorporated into his already successful system of coaching for standardized tests to create a method that not only increased math scores, but simultaneously increased any students' mathematical skill level, whereby increasing their potential score.
Dr. Warner did complete graduate school, earning the TA teaching excellence award in the process, and becoming a successful Professor of Mathematics, first at Penn State and then at Hofstra University where he currently works. During his time at Hofstra he has taught a full range of undergraduate and graduate courses, published several articles in scholarly journals, and participated in a five year, eleven million dollar NSF grant, "The MSTP Project," to improve mathematics and science curriculum in poorly performing middle schools.
In 2012, Dr. Warner founded "GET 800" whose goal it is to provide inexpensive SAT math preparation for students who cannot afford to pay $350 per hour for one on one tutoring from a test prep expert. GET 800 offers 7 SAT math prep books, and a free 12 part email course that is customized for each student based on his or her PSAT/SAT math score.
Dr. Warner works with students individually and in group settings, h
Dr. Warner's philosophy is quite different from most experts in that he focuses on test-specific strategy designed to save time, avoid carelessness, and exploit the weaknesses of standardized tests, as opposed to spending valuable time on the conventional teaching of mathematics. Furthermore, Dr. Warner realizes that students at different score levels must be taught differently and this is reflected very strongly in his materials.
Dr. Warner began tutoring his classmates while he was still in high school, and by the time he started college he had already tutored over 100 students in subjects ranging from algebra to AP calculus. He soon became known as the "math ninja" because of his incredible ability to help students get over a 90 on their tests with just one short tutoring session.
Throughout college Dr. Warner began tutoring more advanced topics such as linear algebra, differential equations and advanced calculus. His ability to get even the weakest math majors to understand deep theoretical concepts became well known throughout the campus. During this time he received several math scholarships and a 4.0 in mathematics, but it wasn't until graduate school that Dr. Warner had an experience which changed his philosophy on teaching forever....
When Dr. Warner began graduate school he actually found himself struggling with the material for the first time. He worked harder than he ever had in the past, but was not able to grasp the concepts as easily as he had as an undergraduate. Dr. Warner finally experienced the feelings that his clients went through. But an interesting thing happened soon after. All of a sudden nothing seemed difficult anymore and he was back at the top of his class. Despite the fact that he was taking even harder classes now, he was once again breezing through them with very little effort.
It was at this time that Dr. Warner had two realizations.
(1) Working harder and long hours does not necessarily lead to more success in mathematics.
(2) It is possible for anyone to increase their skill in mathematics to any level they choose.
You see, during that first year Dr. Warner experimented with many methods to get himself to learn material that was too difficult for him. And eventually he figured it out. It was this final step in his evolution that allowed him to become an even more effective tutor than ever before. What he learned during this process was incorporated into his already successful system of coaching for standardized tests to create a method that not only increased math scores, but simultaneously increased any students' mathematical skill level, whereby increasing their potential score.
Dr. Warner did complete graduate school, earning the TA teaching excellence award in the process, and becoming a successful Professor of Mathematics, first at Penn State and then at Hofstra University where he currently works. During his time at Hofstra he has taught a full range of undergraduate and graduate courses, published several articles in scholarly journals, and participated in a five year, eleven million dollar NSF grant, "The MSTP Project," to improve mathematics and science curriculum in poorly performing middle schools.
In 2012, Dr. Warner founded "GET 800" whose goal it is to provide inexpensive SAT math preparation for students who cannot afford to pay $350 per hour for one on one tutoring from a test prep expert. GET 800 offers 7 SAT math prep books, and a free 12 part email course that is customized for each student based on his or her PSAT/SAT math score.
Dr. Warner works with students individually and in group settings, h
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