Introduction to Mathematical Thinking

Start Date: 07/05/2020

Course Type: Common Course

Course Link:

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About Course

Learn how to think the way mathematicians do – a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box – a valuable ability in today’s world. This course helps to develop that crucial way of thinking.

Course Syllabus

START with the Welcome lecture. It explains what this course is about. (It comes with a short Background Reading assignment, to read before you start the course, and a Reading Supplement on Set Theory for use later in the course, both in downloadable PDF format.) This initial orientation lecture is important, since this course is probably not like any math course you have taken before – even if in places it might look like one! AFTER THAT, Lecture 1 prepares the groundwork for the course; then in Lecture 2 we dive into the first topic. This may all look like easy stuff, but tens of thousands of former students found they had trouble later by skipping through Week 1 too quickly! Be warned. If possible, form or join a study group and discuss everything with them. BY THE WAY, the time estimates for watching the video lectures are machine generated, based on the video length. Expect to spend a lot longer going through the lectures sufficiently well to understand the material. The time estimates for completing the weekly Problem Sets (Quiz format) are a bit more reliable, but even they are just a guideline. You may find yourself taking a lot longer.

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Course Introduction

Introduction to Mathematical Thinking for K-12 Educators This course introduces the key concepts of introductory and algebraic math, with a focus on students' ability to apply these concepts in their classrooms. The course starts with an overview of what elementary and middle school math is and an exploration of the basic ideas behind the basic tools used to construct math problems. This exploration is followed by a tour of the algebraic structure of mathematical problems, including the common ones involving integers, strings, and other primitives. The tour continues with an in-depth analysis of the algebraic modeling needed to solve problems, including the use of surfaces and conditioning. The final part of the course focuses on the algebraic modeling needed to solve the modeling problem, including the use of the formulae and formulas. This course is designed for students who have no prior background in algebra, and it is intended for students who are interested in learning to think critically and creatively. Upon successful completion of this course, you will be able to: 1. Solve simplex and partial differential equations 2. Solve linear and quadratic equations 3. Solve some classes of partial differential equations, including those involving a vector, a time-dependent formulae, and a formulae involving a time-dependent formulae.Introductory Algebraic Mathematics Formulas and Solving Problems

Course Tag

Number Theory Real Analysis Mathematical Logic Language

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