Self-Teaching Theoretical Guide Books of Complex Mathematics
For many students, math is boring, lacking in creativity, complex and very difficult to understand, but mathematics is present in our daily lives. Mathematics has a number of very useful benefits to our mind if we go into its study. It develops our reasoning, helps us to have analytical thinking, quickens our mind, generates practicality and also its use can be applied in the day to day.
If you think you need to learn mathematics by yourself beyond academic education, at first you have to be familiarized with mathematical knowledge and guidelines for easy self-learning. Here we will suggest you some study materials and/or guidebooks that may assist you with your study goals.
Guidebooks for Beginners Related to Pure Mathematical Terms
1. Real Analysis - Sequences and Series
The subject is primarily about real numbers and functions between sets of real numbers. The main topics discussed include sequences, series, convergence, limits, calculus, and continuity. The primary benefit of studying real analysis is that it provides a gentle introduction to proofs.
In order to learn real analysis by yourself, we would like to suggest you take a look at the list of guidebooks below:
- Number and Functions: Steps into Analysis by R.P Burn.
- Real Analysis by John Howie.
- Principles of Mathematical Analysis by Walter Rudin.
The goal of the course is to provide you with a detailed overview of the nature of university mathematics, including the notions of proof (such as proof by induction and proof by contradiction), the concept of a map or function, as well as the different types such as the injection, surjection, and bijection.
Self-study of mathematical foundations can be challenging. Here is a textbook listed for your mathematical foundation.
- The Foundations of Mathematics by Ian Stewart and David Tall.
3. Linear Algebra
Linear Algebra has such wide applicability in mathematics, physics, engineering, and science in general. Hence, there are many great resources available for learning it by yourself.
- Introduction to Linear Algebra, Fourth Edition by Gilbert Strang.
- Basic Linear Algebra by T.S. Blyth and E.F. Robertson.
4. Ordinary Differential Equation
Formally, a differential equation is a relationship between a function and its derivatives. Informally, they are equations, which describe how rates of change of the function, with respect to some other quantity, affect the function itself.
- An Introduction to Ordinary Differential Equations by James Robinson is highly recommended for you to learn about the differential equation.
Geometry is one of the most fundamental areas of mathematics. It is absolutely essential for many areas of deeper mathematics, including those related to quantitative finance. Geometry is a tricky subject. Here we have found the following book to be helpful:
- Geometry by Roger Fenn.
Probability courses naturally lead to more advanced courses on (classical) Statistics, Bayesian Statistics, Stochastic Processes, Stochastic Analysis, Econometrics and Time Series Analysis. The following book on probability is recommended for you.
- A First Course in Probability by Sheldon Ross.
8. Mathematical Computing
This course is carrying out mathematical analysis using computer programs. It is absolutely essential that you gain a grounding in programming algorithms at the earliest possible stage. Though it is difficult to suggest study material for this course, the following books are recommended for you:
- Hands-on Start to Wolfram Mathematica by Cliff Hastings.
- Matlab - A Practical Introduction to Programming and Problem Solving, 3rd Edition by Stormy Attaway.
Classic Mathematics Books for Life-Long Learners
If you want to motivate yourself by learning mathematics, the following books are highly recommended for you.
Both authors are top-rank mathematicians with years of stage performances behind them, and their specialty is mathematical magic. They show how mathematics relates to juggling and reveal the secrets behind some amazing card tricks.
This book is all about mathematical logic.
This book communicated to the world one of the very greatest ideas of all time: Nature has laws, and they can be expressed in the language of mathematics.
A collection of humanistic, semi-technical essays about some of the most fundamental questions and philosophical issues in mathematics, along with the historical development of the various subtopics and peripheral topics in mathematics.
This is a great book that could make almost anyone love math. It covers a lot of world history and begins with humans use of numbers and counting.
A step-by-step guide on how a mathemagician manages to pull off gigantic arithmetic calculations off of the top of his head through a combination of smart tricks and mnemonic techniques.
This book showcases the different mental processes for dissecting a problem and discusses how one can go from a master of tricks into an actual, standalone mathematical thinker.
This book is for you if you are fascinated with imaginary numbers.
If you want to learn about the history of mathematics, this book is for you. This is a beautiful book with short and interesting stories from mathematics history.
Learning mathematics can be made easier and enjoyable if you can develop clear concepts in mathematics.
If you want to know more about this, you can check on Best Algebra and Trigonometry books.