To most students, mathematics is a difficult course. Yet, it has far more to it than just some equations and formulas; indeed, it is a way of thinking, analyzing, and logically approaching problems. From Coursera, the “Introduction to Mathematical Thinking” is there to teach the student not only how to solve mathematical problems but also how to think mathematically. Whether you are a first-time learner of mathematics wanting to build a foundation or more advanced, learning to sharpen your logical reasoning, this course approaches and explores mathematics from a uniquely insightful perspective as a tool for thinking.
This article delves into the course in an exhaustive review: aims and objectives, target audience, unique features, study plan, instructors, certification, price, topics covered, and very detailed FAQs. So, why do learners all over the world love Introduction to Mathematical Thinking?
Introduction
Mathematics is far from simple equations and numbers. It is a universal language that creates the framework with which one frames problems, devises solutions, and reasons logically. The Introduction to Mathematical Thinking course on Coursera is by Stanford University professor Dr. Keith Devlin, who attempts to make learners think for themselves in analytical ways to attack problems relevant to everyday life by applying mathematical ideas. It is not a math class per se. Instead, it is tailored to teach a different approach to thinking about problems and is best for students interested in mathematics, computer science, engineering, or logic.
Course Description
The two primary goals of the course Introduction to Mathematical Thinking are:
- To develop logical and analytical ways of thinking as they are expressed in mathematics and elsewhere.
- To teach students to tackle complex problems using abstract reasoning and mathematical logic.
- By bridging the gap between the mathematical techniques to be developed at the high school level and mathematical thinking at the university level.
- To guide learners to understand and construct proofs, which play an important role in higher-level mathematics.
- Introducing the process of mathematical modeling for helping students alike in academic and professional capacities.
This class isn’t about learning how to do school mathematics like algebra or calculus. It’s more about changing your thinking in a mathematical way applicable to any field.
Course Details
| Course Information | Details |
|---|---|
| Course Name | Introduction to Mathematical Thinking |
| Instructor | Dr Keith Devlin |
| Platform | Coursera |
| Institution | Stanford University |
| Level | Beginner |
| Language | English |
| Prerequisites | None |
| Certifications | Yes only for paid users |
| Enrollment Options | Yes various enrollment options are available |
| Topics Covered | Introduction to Mathematical Concepts and Principles. |
| Key Features | Videos, Quizzes, and Assignments. |
| Duration | 38 hours |
Target Audience
- This course is universal. You will find it useful if you are:
- University Students: If you are moving from a university-level course in mathematics or logic, this course will get you ready for mathematical thinking.
- Aspiring Data Scientists and Engineers: This field boils down to analytical and mathematical thinking. This course provides a foundation for such careers.
- Teachers: Educators looking to teach mathematical logic and reasoning innovatively.
People from any sphere, be it economics, computer science, or engineering, are interested in developing problem-solving abilities.
Please note that the course does not require any deep knowledge of high school mathematics. You should be able to easily trace each step if you are comfortable with basic algebra and logical reasoning.
Study Plan and Duration
It has been designed as flexible, hence fitting for working professionals with hectic schedules. This course is stretched over 9 modules with a suggested engagement of about 38 hours per week as detailed below:
- Week 1: Introduction to Mathematical Thinking
- Introduction to the course and key concepts like problem-solving and logical reasoning.
Week 2: Defining and Being Precise - The use of precise definitions and formal language in mathematical thinking.
- Week 3: Statements and Proofs
- Mathematical statements and the process of building and interpreting proofs.
- Week 4: Quantifiers and Implication
- Logical quantifiers such as “for all” and “there exists” with implications and their application in reasoning.
- Week 5: More on Proofs
- Methods of proof for mathematical theorems and results.
- Week 6: Structures and Invariants
- The role of structure in mathematics, and how invariants make problems more tractable
Week 7: Mathematical Modeling - Using mathematical thinking to build models that explain and predict phenomena in the world around us
- Week 8: Final Reflections
- Review of the course, and how to apply mathematical thinking outside of class.
This structure allows for the gradual development of mathematical reasoning and multiple reflection and practice points.
Key Features
The Introduction to Mathematical Thinking course consists of the following noteworthy features:
- Video Lectures: Dr. Keith Devlin’s video lectures are enjoyable to watch as well as explained in accessible ways for the students to get a good grasp of the course material.
- Interactive Quizzes: For every module, quizzes help reinforce the material and provide learners with immediate feedback.
- Discussion Forums: Learners discuss topics, question each other, and get in touch with other like-minded people.
- Assignments: There is an involvement of regular assignments that encourage learners to work out various real-life and theoretical applications.
Pros and Cons
Pros:
- Interactive Learning: Dr. Devlin, well known to the world as the “Math Guy,” presents content in an engaging and easy-to-learn manner.
- General Utilization: This is not strictly mathematics; it aids in the development of critical thinking skills that are useful in other fields.
- Flexibility: Self-paced nature allows the learner to study it at his convenience. Hence, this course is a good resource for working professionals or busy students.
Cons
- Not Found to be Calculative: It may lack here as students might expect algebraic or calculus-based traditional problems.
- May Require Patience: Mathematical thinking is not with time; however, learners are likely to be patient with the learning curve.
Instructors and Their Background
Lecturer: Dr. Keith Devlin is a professor at Stanford University and a recognized leader in the field of mathematical cognition, he has written over 30 books, and he has played an important role in changing mathematical developments in a manner to make math accessible to thousands of people. He’s able to be extremely clear and entertainingly teach and share his many years of experience and deep knowledge of mathematical reasoning, bringing that knowledge alive in the lectures.
His outreach activities go beyond the campus setting as he frequently appears on NPR under the name “Math Guy,” and has also written extensively about how math interacts with daily life.
Certification
After finishing this course you will get a certificate that will be important for your future job prospects.
Pricing
There are two pricing options available on Coursera for this course:
- Audit Free: Learners have access for free to the material and video lectures. Still, no certificate will be provided nor an opportunity to complete graded assignments.
- Paid Option: For about $49, learners have access to graded assignments, quizzes, and peer-reviewed projects, and they receive a certificate when the course is completed. For the price of Coursera, financial aid is also available in case the learner is not so capable and needs that support.
Topics Included
- Basics of Mathematical Fundamentals
- Precision and Definition: Why is precision in language and definition important to mathematics?
- Statements and Proofs: How do mathematical statements work and how do you build proofs?
- Quantifiers and Implication: How the logical quantifiers and implications work in establishing an argument.
- Structures and Invariants: How structures and invariants can be used to simplify complicated problems.
- Mathematical Modeling: Using mathematical thinking to solve real-world problems through modeling.
How to Enroll for this course
There’s nothing complex in the enrollment procedure for this course:
- Navigate to the course page at Coursera
- Click the option Enroll for Free
- Both audit versions are free, but you can also pay for the for-credit course with certification
- You’ll be asked to create a Coursera account if this is the first time registering or sign in if you already have an account
- Once enrolled, start learning at your own pace!
FAQ’s
Q1: Does this course require any experience in maths?
A: Definitely, as this course is designed for beginner students and even introduces concepts in maths in simple step-by-step ways this course teaches you everything from basics and this course is self-paced and flexible.
Q2: Are there free versions of this course?
A: Yes there are free versions available but the certificate is not available in the free version only the paid version is available you can audit this course for free and various pricing options are available for this course.
Q3: Does this course help me, if am weak at maths?
A: Yes, it covers special plans, videos on maths concepts, and various techniques to help you stay focused there are quizzes for practice as well and this course is well-structured with detailed videos and assignments.
Q4: What is the duration of this course?
A: It takes approximately 38 hours to complete, depending on learner speed and the time taken to complete this course, and depending on the study plan the course can be learned accordingly.
Q5: Is there any Financial aid?
A: Any learner who qualifies for financial aid gets access to the paid version of the course as well as a certificate will be provided for the paid version of this course thus various EMI options are available for this course.
Conclusion
One great course on Coursera is the Introduction to Mathematical Thinking course, which builds both logical and critical thinking. To be honest, I’m not at all interested in solving usual mathematical problems, but because it teaches how to approach problems like a mathematician more than trying to solve them, it is highly useful in many disciplines, such as computer science, data science, engineering, and economics.
This course is a must for all who wish to sharpen their analytical skills through Dr. Keith Devlin’s expertise and teaching style. Whether you are a student preparing for university-level math, a professional looking to improve your problem-solving capabilities, or you are simply one interested in thinking more critically, this course is well-recommended.
By the time they complete the course, learners will no longer only appreciate mathematics more profoundly, but they will also achieve a dynamic set of thought skills to use in complex challenges in every walk of life.
