The ability to think logically and decipher trends is a rare skill. But if you can use mathematics to describe our world, or are interested in learning, then you may be on track for a range of successful careers.
Below, we’ve compiled a complete guide for learning about mathematical thinking and making a career decision that involves this skill. These resources cover what mathematical thinking involves, free online courses on the topic, and information to enhance your logical reasoning capabilities.
What Is Mathematical Thinking?
Mathematical thinking is all about thinking outside of the box. While math you learn in grade school typically focuses on textbook problems, mathematical thinking looks at issues from a wider angle to apply logic and find novel solutions.
What Is Mathematical Thinking Used For?
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Mathematical thinking has a wide range of applications for actuaries, engineers, and others. Below are some examples of areas where mathematical thinking is used.
- Data analysis. Mathematical thinking is used for data analysis. It allows you to differentiate between different sets of information. Furthermore, it enables you to choose procedures and techniques efficiently.
- Validating theorems. Mathematical thinking is an important requirement in reverse engineering and is used to deduce how results relate to established claims.
- Computer science programming: This skill is necessary for software engineers. These professionals must use strict logical thinking while coding.
- Financial risk analysis. Investment bankers and risk analysts use mathematical thinking to calculate the likely outcomes of a decision. They also use it to determine marginal values through correct functions.
Types of Mathematical Thinking
Mathematical thinking is divided into three categories. Keep reading to explore what these include.
Spatial or Geometric Reasoning
Spatial imagination is the ability to imagine objects and images as well as mentally modify them and analyze their nature. A broad body of research concludes that spatial reasoning is closely related to mathematical problem-solving.
Learning geometric reasoning is the ultimate achievement for mathematics students. Math competitions often require the use of this skill.
Computational thinking helps you solve complex problems. These solutions can be interpreted by a machine, person, or both. This type of reasoning breaks down problems into more manageable chunks.
These smaller problems can then be evaluated separately. This approach maximizes the chances of reaching a problem’s solution.
Logical or Scientific Reasoning
One of the most essential skills is the ability to think logically. It involves the process of observation, grouping, postulating, experimenting, and inductive and deductive thinking High standard reasoning is known as logical or critical thinking.
These skills can be developed and enhanced. Logical thinking includes three types: inductive reasoning, deductive reasoning, and abductive reasoning.
Learning Mathematical Thinking
Mathematical thinking is a unique ability that can add significant weight if included in your resume’s skill section. Learning mathematical thinking will definitely provide you an edge over other applicants when applying for the same job.
You can learn mathematical thinking either by attending in-person training classes or online courses. A complete list of all the best options available for you is provided below along with extra resources to help you out on your learning journey.
How Long Does It Take to Learn Mathematical Thinking?
However, there are many standalone courses to learn this skill. You can join an online course, for example. Using this resource you can learn about the fundamentals of mathematical thinking in less than a week.
How to Learn Mathematical Thinking: Step-by-Step
Learning mathematical thinking can be an enjoyable activity for enthusiasts of math. Below is a step-by-step guide on how to think mathematically.
- Choose a course. First, pick an online or conventional training program that fits your schedule.
- Enroll. Don’t waste time, get enrolled and begin your preparation.
- Learn to reason. Mathematical thinking is applied in a variety of fields. You must develop the habit of seeing the world logically and apply mathematics to real-world things.
- Increase your knowledge. Books and text will give you a needed kick-start in learning. Check out our recommendations below to study mathematical thinking on your own time.
- Learn to apply mathematical tools. Mathematics can be used to interpret and solve many problems. But knowing which mathematical tools to apply is necessary. For example, you’ll need to learn calculus, regressions, and induction.
The Best Mathematical Thinking Courses and Training
Below are some great globally respected on-campus courses. They will help you pursue the ability to think mathematically full time.
Best In-Person Training Programs
If you are not comfortable with the concept of online learning and prefer a one to one learning environment, then you can go for an in-person training program. Below we have mentioned the best in-person courses available for you.
University of Delaware, USA
- Course name: MS in Applied Mathematics
- Fee: $34,134
- Duration: 2 years
- Pre requisites: Bachelor’s degree
This program will teach you how to use different mathematical tools. The curriculum includes numerical analysis, computer simulation, and applications for real-world scenarios. This is a two-year program offered by the University of Delaware.
Indiana University Purdue University Indianapolis, USA
- Course name: Masters in Applied Mathematics
- Fee: $19,805
- Duration: 2 years
- Prerequisites: Bachelor’s degree
This course focuses on the application of mathematical thinking in various industries. The curriculum includes fluid mechanics, optimal design, and propagation of waves. This two-year program offered at Indiana University will prepare you for leading research projects.
Online Mathematical Thinking Courses
Learning a skill through online courses is one of the most optimal by providing you with large amounts of flexibility.
- Course: Introduction to Mathematical Thinking
- Duration: Approx. 39 hours
- Prerequisites: None
- Fee: $30
This course offered by Stanford University will help you to develop the different skills you need to master to learn mathematical thinking like number theory, real analysis and mathematical logic. The course also provides you a certification on behalf of Stanford University.
- Course name: Effective Thinking Through Mathematics
- Fee: $49
- Duration: 4 weeks
- Prerequisites: High school mathematics
This course offers techniques for successful and innovative thinking. These lessons are taught using mathematical concepts.
- Course: A Transition to Higher Mathematics
- Duration: 5 hours
- Prerequisites: None
- Fee: $4.87
In this course, you will learn calculus, numerical methods, algebra, real analysis, and several other topics. It also teaches reasoning including conditional and biconditional statements. If you are looking to embrace thinking mathematically, then this is the perfect course for you.
Free Mathematical Thinking Online Courses
These are a few of the top free online certification courses to learn how to think mathematically.
- Course: Coursera
- Duration: 39 hours
- Prerequisites: None
- Fee: Free
Mathematical thinking is very different from mathematics itself. School math is usually based on learning a method to solve theoretical problems. But qualified mathematicians solve real issues from nature or within the field itself.
This course will help you develop a tendency to analyze issues mathematically. It will also teach you to learn the language of mathematics and real analysis.
- Provider: Coursera
- Duration: 37 hours
- Prerequisites: None
- Fee: Free
This course features the application of mathematical thinking along a range of disciplines. You’ll learn induction, recurrence, reasoning, variables, illustrations, and accuracy. In addition, the program also provides puzzles and illustrations to help you invent concepts and tricks of your own.
Best Mathematical Thinking Books
Books are the best source of knowledge when it comes to learning mathematical thinking. There are hundreds of mathematical thinking books available. But how do you know which one is worth your time? Below we have mentioned the best books for mathematical thinking to help you out in your selection.
This book is for first and second-year students in science, technology, engineering, and mathematics (STEM). It can serve as a textbook or an additional resource. It’s written in a straightforward way and easily accessible.
This is one of Bill Gates’ favorite books. It breaks the myth that mathematics is only about made-up problems in textbooks. Math helps everyone see the secret mechanisms beneath the messy and confusing surface of our planet.
And it introduces shocking discoveries using the mathematician’s method of evaluating life. It also reveals difficult perspectives of the academic community.
Upon reading this book you can develop an array of tools to help you unlock mathematical concepts. You will learn theorems and proofs, solve models, and effectively apply mathematics.
This book includes all major methods of proof-direct methods, instances, inductions, contradictions and contrapositives. This is the perfect book if you are looking for a head-start in your mathematics degree.
A Mind for Numbers gives you a clearer understanding of mathematical thinking. Written by professor of engineering, Barbara Oakley, it is for people struggling with mathematics. She guides her readers to understanding the fundamentals. This book also helps you learn secret tricks to apply mathematics.
Online Mathematical Thinking Resources
There are ample resources available throughout the web if you wish to learn and master thinking mathematically. We have listed a few below for you to check out.
Askiitians.com is a great portal for accessing learning resources. They have a wide range of free and easily accessible notes. The material has been compiled by reputed professors around the globe.
YouTube is an excellent source for learning. To deepen your understanding and interest of mathematical thinking, browse channels like The Royal Institution and Bob Trenwith.
Should You Study Mathematical Thinking?
Mathematical thinking is an extremely complex activity but can be very fruitful in academia or business.
Using mathematical thinking to solve real problems is a vital skill. Mathematics is an important tool to understand the world. And having a mathematics background will put you ahead of your peers.
According to payscale.com, the mean salary for a person who can apply mathematical thinking ranges between $48,000 to $112,000. It’s a highly rewarding skill and demand is constantly growing within research and development.
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