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-Beginners 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-beginner" 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-Beginners is perfect forstudents wishing to begin 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 Beginners. A student with a lower level of mathematical maturity will probably find this book more challenging. However, the reward will certainly be more than worth the effort.Pure Math Pre-Beginner 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 Prime 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 begin learning advanced mathematics, but that are not quite ready to start writing proofs,Students who want to increase their level of mathematical maturity


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