Pure Mathematics For Pre-Beginners

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-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