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Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, Linear Algebra What you'll learn Logic Set Theory Abstract Algebra Number Theory Real Analysis Topology Complex Analysis Linear Algebra Requirements No prerequisites Description Pure Mathematics for Pre-Bners consists of a series of lessons in Logic, Set Theory, Abstract Algebra, Number Theory, Real Analysis, Topology, Complex Analysis, and Linear Algebra. The 8 lessons in this course cover elementary material from each of these 8 topics. A “pre-bner" is a math student that is ready to start learning some more advanced mathematics, but is not quite ready to dive into proofwriting. Pure Mathematics for Pre-Bners is perfect forstudents wishing to b learning advanced mathematics, but that are not quite ready to start writing proofs.high school teachers that want to expose their students to the ideas of advanced mathematics without getting into mathematical rigor.professors that wish to introduce higher mathematics to non-stem majors.The material in this math course includes:8 lessons in 8 subject areas.Examples and exercises throughout each lesson.A problem set after each lesson arranged by difficulty level.There are no prerequisites for this course. The content is completely self-contained. Furthermore, this course will naturally increase a student’s level of “mathematical maturity.” Although there is no single agreed upon definition of mathematical maturity, one reasonable way to define it is as “one’s ability to analyze, understand, and communicate mathematics.” A student with a very high level of mathematical maturity may find this course very easy—this student may want to go through the course quickly and then move on to Pure Mathematics for Bners. A student with a lower level of mathematical maturity will probably find this book more challeg. However, the reward will certainly be more than worth the effort.Pure Math Pre-Bner Book Table Of Contents (Selected) Here's a selection from the table of contents:Lesson 1 - LogicLesson 2 - Set TheoryLesson 3 - Abstract AlgebraLesson 4 - Number TheoryLesson 5 - Real AnalysisLesson 6 - TopologyLesson 7 - Complex AnalysisLesson 8 - Linear Algebra Overview Section 1: Lesson 1 - Logic Lecture 1 Statements Lecture 2 Truth Assignments Lecture 3 Logical Connectives Lecture 4 Evaluating Truth Lecture 5 Logical Equivalence Lecture 6 Tautologies and Contradictions Section 2: Lesson 2 - Set Theory Lecture 7 Describing Sets Explicitly Lecture 8 Describing Sets with Ellipses Lecture 9 Describing Sets with Properties Lecture 10 Cardinality of a Finite Set Lecture 11 Subsets and Proper Subsets Lecture 12 Power Sets Lecture 13 Basic Set Operations Section 3: Lesson 3 - Abstract Algebra Lecture 14 Binary Operations and Closure Lecture 15 Associativity, Commutativity, and Semigroups Lecture 16 Identity and Monoids Lecture 17 Inverses and Groups Lecture 18 Distributivity and Rings Lecture 19 Fields Section 4: Lesson 4 - Number Theory Lecture 20 Divisibility Lecture 21 P Numbers Lecture 22 The Division Algorithm Lecture 23 GCD and LCM Lecture 24 GCD and LCM Continued Lecture 25 The Euclidean Algorithm Section 5: Lesson 5 - Real Analysis Lecture 26 Ordered Sets Lecture 27 Ordered Rings and Fields Lecture 28 Why Isn't Q Enough? Lecture 29 Completeness Section 6: Lesson 6 - Topology Lecture 30 Intervals of Real Numbers Lecture 31 More Set Operations Lecture 32 Open Sets in R Lecture 33 Closed Sets in R Section 7: Lesson 7 - Complex Analysis Lecture 34 The Complex Field Lecture 35 Absolute Value and Distance Lecture 36 Basic Topology of C Section 8: Lesson 8 - Linear Algebra Lecture 37 Matrices Lecture 38 Vector Spaces Over Fields Students wishing to b learning advanced mathematics, but that are not quite ready to start writing proofs,Students who want to increase their level of mathematical maturity HomePage:
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