Start Date: 07/05/2020
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/mathematical-thinking
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.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.
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.
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
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Friedrich Waismann | In "Introduction to Mathematical Thinking: The Formation of Concepts in Modern Mathematics" (1936), Waismann argued that mathematical truths are true by convention rather than being necessarily (or verifiably) true. His collected lectures, "The Principles of Linguistic Philosophy" (1965), and "How I See Philosophy" (1968, ed. R. Harré), a collection of papers, were published posthumously. |
Introduction to Mathematical Philosophy | Introduction to Mathematical Philosophy is a book by Bertrand Russell, published in 1919, written in part to exposit in a less technical way the main ideas of his and Whitehead's "Principia Mathematica" (1910–1913), including the theory of descriptions. |
Visual thinking | Thinking in mental images is one of a number of other recognized forms of non-verbal thought, such as kinesthetic, musical and mathematical thinking. |
Critical thinking | Critical thinking is an important element of all professional fields and academic disciplines (by referencing their respective sets of permissible questions, evidence sources, criteria, etc.). Within the framework of scientific skepticism, the process of critical thinking involves the careful acquisition and interpretation of information and use of it to reach a well-justified conclusion. The concepts and principles of critical thinking can be applied to any context or case but only by reflecting upon the nature of that application. Critical thinking forms, therefore, a system of related, and overlapping, modes of thought such as anthropological thinking, sociological thinking, historical thinking, political thinking, psychological thinking, philosophical thinking, mathematical thinking, chemical thinking, biological thinking, ecological thinking, legal thinking, ethical thinking, musical thinking, thinking like a painter, sculptor, engineer, business person, etc. In other words, though critical thinking principles are universal, their application to disciplines requires a process of reflective contextualization. |
Introduction to Arithmetic | The book Introduction to Arithmetic (, "Arithmēticḕ eisagōgḗ") is the only extant work on mathematics by Nicomachus (60–120 AD). It contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics. Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. |
Introduction | Introduction, The Introduction, Intro, or The Intro may refer to: |
Introduction to Mathematical Philosophy | Mathematics and logic, historically speaking, have been entirely distinct studies. Mathematics has been connected with science, logic with Greek. But both have developed in modern times: logic has become more mathematical and mathematics has become more logical. The consequence is that it has now become wholly impossible to draw a line between the two; in fact, the two are one. They differ as boy and man: logic is the youth of mathematics and mathematics is the manhood of logic. This view is resented by logicians who, having spent their time in the study of classical texts, are incapable of following a piece of symbolic reasoning, and by mathematicians who have learnt a technique without troubling to inquire into its meaning or justification. Both types are now fortunately growing rarer. So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premises which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of "Principia Mathematica", they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary. (Russell 1919, 194–195). |
Mathematical anxiety | Reflective journals help students develop metacognitive skills by having them think about their understanding. According to Pugalee, writing helps students organize their thinking which helps them better understand mathematics. Moreover, writing in mathematics classes helps students problem solve and improve mathematical reasoning. When students know how to use mathematical reasoning, they are less anxious about solving problems. |
Advanced Introduction to Finality | This is the second "Introduction to Finality" episode of the series, following season three's finale, "Introduction to Finality". |
Mathematical Alphanumeric Symbols | The introduction date of some of the more commonly used symbols can be found in the Table of mathematical symbols by introduction date. |
Mathematical psychology | During the war, developments in engineering, mathematical logic and computability theory, computer science and mathematics, and the military need to understand human performance and limitations, brought together experimental psychologists, mathematicians, engineers, physicists, and economists. Out of this mix of different disciplines mathematical psychology arose. Especially the developments in signal processing, information theory, linear systems and filter theory, game theory, stochastic processes and mathematical logic gained a large influence on psychological thinking. |
Vertical thinking | Introduction of these concepts to a child are said to be most useful from the ages 4 onward. When considering existing adolescent trends with regards to cognitive development, it is around the age of 4 that individuals begin to realize that thoughts may not always be true. This is the around the age where the ability to acquire knowledge through induction occurs for the child. Thus, the ability to think sequentially (in this case being classified as vertical thinking) is a concept that will begin to resonate with the child. Due to the fact that individuals generally affiliate themselves with a single method of thinking, being either vertical or later, Paul Sloane suggests the introduction of such situation puzzles at a young age. This is said to help stimulate the type of thinking the child would otherwise not be comfortable with. |
Mathematical economics | Formal economic modeling began in the 19th century with the use of differential calculus to represent and explain economic behavior, such as utility maximization, an early economic application of mathematical optimization. Economics became more mathematical as a discipline throughout the first half of the 20th century, but introduction of new and generalized techniques in the period around the Second World War, as in game theory, would greatly broaden the use of mathematical formulations in economics. |
Introduction to Film | Around 5.86 million Americans watched "Introduction to Film". |
Vertical thinking | This instrument, otherwise known as the SO-LAT, evaluates analytic versus holistic thinking styles. The analytic thinking mode can be compared to vertical thinking, whereas holistic thinking can be compared to lateral thinking. |
Mathematical game | Mathematical games differ sharply from mathematical puzzles in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or mathematical aspects. |
Thinking machine | Thinking machine or thinking machines may refer to: |
Design thinking | Design thinking employs divergent thinking as a way to ensure that many possible solutions are explored in the first instance, and then convergent thinking as a way to narrow these down to a final solution. Divergent thinking is the ability to offer different, unique or variant ideas adherent to one theme while convergent thinking is the ability to find the "correct" solution to the given problem. Design thinking encourages divergent thinking to ideate many solutions (possible or impossible) and then uses convergent thinking to prefer and realize the best resolution. |
Michael Starbird | He has produced DVD courses for The Teaching Company in the Great Courses Series on calculus, statistics, probability, geometry, and the joy of thinking, which have reached hundreds of thousands of people worldwide. Since 2000, he has given over 200 invited lectures and presented more than 35 workshops on effective teaching to faculty members. He has co-authored two Inquiry Based Learning textbooks published by the MAA: (with David Marshall and Edward Odell) Number Theory Through Inquiry and (with Brian Katz) Distilling Ideas: An Introduction to Mathematical Thinking in the new Mathematics Through Inquiry subseries of the MAA Textbook Series. He has written three books with co-author Edward B. Burger: The Heart of Mathematics: An invitation to effective thinking (in its 4th edition and winner of a Robert Hamilton book award); Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas (which has been translated into eight languages); and The 5 Elements of Effective Thinking (which is published by Princeton University Press, has translation contracts in 16 languages, and was a 2013 Independent Publisher Book Award Silver Medal winner). The book, "The Heart of Mathematics: An Invitation to Effective Thinking" was acclaimed by the American Mathematical Monthly as possibly the best math book for nonmathematicians it had ever reviewed. It won a 2001 Robert W. Hamilton Book Award. |
Mathematical sociology | Sociologist, James S. Coleman embodied this idea in his 1964 book "Introduction to Mathematical Sociology", which showed how stochastic processes in social networks could be analyzed in such a way as to enable testing of the constructed model by comparison with the relevant data. In addition, Coleman employed mathematical ideas drawn from economics, such as general equilibrium theory, to argue that general social theory should begin with a concept of purposive action and, for analytical reasons, approximate such action by the use of rational choice models (Coleman, 1990). This argument provided impetus for the emergence of a good deal of effort to link rational choice thinking to more traditional sociological concerns involving social structures. |