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Effective Thinking Through Mathematics

A wondrously romantic belief is that brilliant thinkers magically produce brilliant ideas: Einstein jostles his hair and relativity falls out. We can enjoy these fanciful visions of leaps of genius, but we should not be fooled into believing that they’re reality.

Brilliant innovators are brilliant because they practice habits of thinking that inevitably carry them step by step to works of genius. No magic and no leaps are involved.

Professor Starbird will discuss how practices of effective thinking and creativity can be taught and learned through puzzles and mathematics. Anyone who practices these habits of mind will inevitably create new insights, new ideas, and new solutions.

What you'll learn

Engage in thinking about mathematical ideas
Apply effective strategies of thinking to approach questions in your lives with insight and innovation
Think more effectively and imaginatively throughout your lives

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What's inside

Learning objectives

Engage in thinking about mathematical ideas
Apply effective strategies of thinking to approach questions in your lives with insight and innovation

Think more effectively and imaginatively throughout your lives

Engage in thinking about mathematical ideas
Apply effective strategies of thinking to approach questions in your lives with insight and innovation
Think more effectively and imaginatively throughout your lives

Syllabus

The whole course presents strategies of effective thinking that can make you more creative and more insightful. These overarching lessons are conveyed through fascinating mathematical themes. Weeks 1 and 2 – An Introduction and Puzzles These two weeks provide an introduction to the course and introduce five practical elements of effective thinking. By working on fun puzzles, you will use these practices of mind to create insights and solve conundrums. The basic theme is that more effective problem-solving arises from employing learnable ways of thinking. Weeks 3-4 – Infinity Here you will take a dramatic journey that begins with the most basic concept of number and lets you personally move logically to an understanding of infinity... and beyond! Throughout you will see how amazing insights about the infinite flow from strategies of effective thinking. Week 5 – The Koenigsberg Bridge Puzzle and Conclusion Specific challenges can lead to general insights. A puzzle from the 1730's leads from walking over bridges to wonderful mathematical insights. Most importantly, all these explorations illustrate methods of thinking that are applicable to your own life.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Builds a strong foundation for beginners in effective thinking, puzzle-solving, and mathematical concepts

Taught by Michael Starbird, a professor recognized for their work in effective thinking and creativity

Develops effective thinking strategies that are applicable to problem-solving in various life situations

Uses engaging mathematical themes to convey overarching lessons on effective thinking

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Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Effective Thinking Through Mathematics with these activities:

Review foundational math concepts

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Reinforce your understanding of basic mathematical concepts to prepare for more advanced topics in the course.

Browse courses on Mathematical Thinking

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Review arithmetic operations (addition, subtraction, multiplication, division)
Practice solving simple algebraic equations
Recall key concepts from geometry such as area, volume, and shapes

Read 'Thinking and Problem Solving'

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Gain a deeper understanding of thinking strategies and problem-solving techniques to enhance your cognitive abilities.

View Teaching for Wisdom, Intelligence, Creativity,... on Amazon

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Acquire a copy of the book
Read the book thoroughly and take notes
Reflect on the concepts and apply them to your own experiences

Organize a study group with peers

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Enhance your learning through collaboration by forming a study group with peers to discuss course concepts, solve problems, and support each other.

Browse courses on Collaboration

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Reach out to fellow students and form a study group
Establish regular meeting times and a designated study space
Take turns presenting concepts, leading discussions, and solving problems

Five other activities

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Solve logic puzzles

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Engage in solving logical puzzles to sharpen your critical thinking and problem-solving abilities.

Browse courses on Logical Reasoning

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Attempt to solve Sudoku or crossword puzzles
Engage in online quizzes or games that test logical reasoning

Attend a workshop on mathematical problem-solving techniques

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Gain insights and learn strategies by attending a workshop specifically designed to enhance problem-solving abilities in mathematics.

Browse courses on Problem Solving

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Research and identify a relevant workshop
Register and participate in the workshop
Engage actively, ask questions, and take notes

Create a visual representation of a mathematical concept

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Enhance your understanding by visually representing a mathematical concept to improve retention and recall.

Browse courses on Data Visualization

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Choose a mathematical concept you find challenging
Sketch or draw a visual representation of the concept using diagrams, graphs, or charts
Explain your visual representation to a peer or family member

Explore online tutorials on advanced mathematical topics

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Expand your knowledge by exploring online tutorials that delve into more advanced mathematical topics to supplement the course material.

Browse courses on Mathematical Concepts

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Identify a specific mathematical topic you want to explore further
Search for reputable online tutorials or courses covering the topic
Follow the tutorials, take notes, and engage in any interactive exercises

Contribute to an open-source mathematics project

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Engage in practical application and contribute to the wider mathematical community by participating in an open-source project related to mathematics.

Browse courses on Open Source

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Identify an open-source mathematics project that aligns with your interests
Review the project documentation and identify areas where you can contribute
Reach out to the project maintainers and express your interest in contributing

Career center

Learners who complete Effective Thinking Through Mathematics will develop knowledge and skills that may be useful to these careers:

Actuary

Actuaries leverage advanced mathematical concepts such as algebra and statistics to analyze statistical and financial data. There is significant overlap between the elements of effective thinking that actuaries use to solve complex risk management problems and those taught in this course, such as inductive reasoning and lateral thinking. These skills are vital to success in actuarial work, where the ability to identify and understand relevant patterns and make well-informed predictions allows professionals to thrive within this discipline.

See salaries and explore the career path for Actuary

Data Analyst

Data analysts use mathematical and statistical techniques to extract insights from data. This course would be very helpful to someone working in data analysis, as it teaches effective strategies of thinking that can be applied to approach questions with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help data analysts develop a deeper understanding of mathematical concepts and their applications in the real world.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial analysts use mathematical and statistical models to analyze financial data and make investment recommendations. This course would be helpful to someone working as a financial analyst, as it teaches effective strategies of thinking that can be applied to approach financial problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help financial analysts develop a deeper understanding of mathematical concepts and their applications in the world of finance.

See salaries and explore the career path for Financial Analyst

Market Researcher

Market researchers use mathematical and statistical techniques to collect and analyze data about consumer behavior. This course would help teach someone working as a market researcher to think more creatively and to approach problems in a more logical and analytical manner. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help market researchers develop a deeper understanding of mathematical concepts and their applications in market research.

See salaries and explore the career path for Market Researcher

Operations Research Analyst

Operations research analysts use mathematical and statistical techniques to improve the efficiency of business operations. This course may be useful to someone working as an operations research analyst, as it teaches effective strategies of thinking that can be applied to approach operational problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help operations research analysts develop a deeper understanding of mathematical concepts and their applications in business.

See salaries and explore the career path for Operations Research Analyst

Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course would be very useful to someone working as a quantitative analyst, as it teaches effective strategies of thinking that can be applied to approach financial problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help quantitative analysts develop a deeper understanding of mathematical concepts and their applications in finance.

See salaries and explore the career path for Quantitative Analyst

Software Engineer

Software engineers use mathematical and logical thinking to design and develop computer software. This course would be helpful to someone working as a software engineer, as it teaches effective strategies of thinking that can be applied to approach software development problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help software engineers develop a deeper understanding of mathematical concepts and their applications in software development.

See salaries and explore the career path for Software Engineer

Statistician

Statisticians use mathematical and statistical techniques to collect and analyze data. This course would be very helpful to someone working as a statistician, as it teaches effective strategies of thinking that can be applied to approach statistical problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help statisticians develop a deeper understanding of mathematical concepts and their applications in statistics.

See salaries and explore the career path for Statistician

Teacher

Teachers use mathematical and logical thinking to teach students about a variety of subjects. This course would be helpful to someone working as a teacher, as it teaches effective strategies of thinking that can be applied to approach teaching problems with insight and innovation. The course covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help teachers develop a deeper understanding of mathematical concepts and their applications in education.

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Economist

Economists use mathematical and statistical techniques to analyze economic data and make recommendations for economic policy. This course would be helpful to someone working as an economist, as it teaches effective strategies of thinking that can be applied to approach economic problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help economists develop a deeper understanding of mathematical concepts and their applications in economics.

See salaries and explore the career path for Economist

Financial Manager

Financial managers use mathematical and statistical techniques to manage financial resources. This course would be helpful to someone working as a financial manager, as it teaches effective strategies of thinking that can be applied to approach financial management problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help financial managers develop a deeper understanding of mathematical concepts and their applications in financial management.

See salaries and explore the career path for Financial Manager

Investment Banker

Investment bankers use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course would be helpful to someone working as an investment banker, as it teaches effective strategies of thinking that can be applied to approach investment banking problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help investment bankers develop a deeper understanding of mathematical concepts and their applications in investment banking.

See salaries and explore the career path for Investment Banker

Management Consultant

Management consultants use mathematical and logical thinking to help businesses solve problems and improve performance. This course would be helpful to someone working as a management consultant, as it teaches effective strategies of thinking that can be applied to approach management consulting problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help management consultants develop a deeper understanding of mathematical concepts and their applications in management consulting.

See salaries and explore the career path for Management Consultant

Operations Manager

Operations managers use mathematical and logical thinking to improve the efficiency of business operations. This course may be useful to someone working as an operations manager, as it teaches effective strategies of thinking that can be applied to approach operations management problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help operations managers develop a deeper understanding of mathematical concepts and their applications in operations management.

See salaries and explore the career path for Operations Manager

Product Manager

Product managers use mathematical and logical thinking to develop and manage products. This course may be useful to someone working as a product manager, as it teaches effective strategies of thinking that can be applied to approach product management problems with insight and innovation. The course also covers topics such as infinity and the Koenigsberg Bridge Puzzle, which can help product managers develop a deeper understanding of mathematical concepts and their applications in product management.

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Reading list

We've selected 22 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Effective Thinking Through Mathematics.

The Heart of Mathematics: an Invitation to...

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This is the textbook for the course. It presents the course's materials in a detailed and organized manner.

Effective Thinking Through Mathematics

What you'll learn

What's inside

Learning objectives

Syllabus

Good to know

Save this course

Activities

Career center

Reading list

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