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 for
students 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 - Logic
Lesson 2 - Set Theory
Lesson 3 - Abstract Algebra
Lesson 4 - Number Theory
Lesson 5 - Real Analysis
Lesson 6 - Topology
Lesson 7 - Complex Analysis
Lesson 8 - Linear Algebra
