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The Definitive Guide to Learning Higher Mathematics

Author: Math Vault

Publisher: Math Vault Publishing

Published: 2018-11-01

Total Pages: 86

ISBN-13:

The Definitive Guide to Learning Higher Mathematics is a comprehensive, illustrated guide to help you optimize higher mathematical learning, thinking and problem solving through 10 foundational principles and countless actionable tips. In 10 chapters and 86 pages, it’ll take you around the different aspects of higher mathematical learning, leaving no stone unturned from material selection, big picture thinking, proximal zone, cognitive techniques to proactive learning, head-processing, scientific method and social learning. Hightlights - Extensive actionable tips to illustrate each principle involved - Extensive annotations, pro-tips, quotes and illustrations for better insight - Carefully prepared after-chapter summaries for better understanding - Printable PDF format (8.5 in. x 11 in.) with linkable table of contents and index for handy reference and reviewing Table of Contents 0. Preface 1. Choose Your Materials Judiciously 2. Always Keep the Big Picture in Mind 3. Operate within the Proximal Zone 4. Isolate Until Mastered Before Moving On 5. Be a Proactive, Independent Thinker and Learner 6. Do Most Things Inside Your Head 7. Practice the Scientific Method in a Creative Way 8. Don’t Fret Too Much About Real-life Applicability 9. Scale Up Learning by Going Social 10. Embrace the Mathematical Experience 11. Last Few Words 12. Index

An Accompaniment to Higher Mathematics

Author: George R. Exner

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 212

ISBN-13: 1461239982

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Designed for students preparing to engage in their first struggles to understand and write proofs and to read mathematics independently, this is well suited as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology. The book teaches in detail how to construct examples and non-examples to help understand a new theorem or definition; it shows how to discover the outline of a proof in the form of the theorem and how logical structures determine the forms that proofs may take. Throughout, the text asks the reader to pause and work on an example or a problem before continuing, and encourages the student to engage the topic at hand and to learn from failed attempts at solving problems. The book may also be used as the main text for a "transitions" course bridging the gap between calculus and higher mathematics. The whole concludes with a set of "Laboratories" in which students can practice the skills learned in the earlier chapters on set theory and function theory.

Visible Learning for Mathematics, Grades K-12

Author: John Hattie

Publisher: Corwin Press

Published: 2016-09-15

Total Pages: 209

ISBN-13: 1506362958

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Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction...with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings. Deep learning phase: When—through the solving of rich high-cognitive tasks and rigorous discussion—students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency. Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. To equip students for higher-level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K-12 through intentionally designed guided, collaborative, and independent learning.

A Transition to Advanced Mathematics

Author: William Johnston

Publisher: Oxford University Press

Published: 2009-07-27

Total Pages: 768

ISBN-13: 9780199718665

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A Transition to Advanced Mathematics: A Survey Course promotes the goals of a "bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-level mathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey'' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, Abstract Algebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability to communicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. The text has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embedded reflections on the history, culture, and philosophy of mathematics throughout the text.

Higher Mathematics from an Elementary Point of View

Author: RADEMACHER

Publisher: Birkhäuser

Published: 2013-09-11

Total Pages: 138

ISBN-13: 9781489949790

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Comprehensive List of Mathematical Symbols

Author: Math Vault

Publisher: Math Vault Publishing

Published: 2020-06-13

Total Pages: 76

ISBN-13:

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Ever wonder if there's a reference guide out there summarizing most of the symbols used in mathematics, along with contextual examples and LaTeX code so that you can pick up the various topics of mathematics at an unusual speed? Well now there is! In this jam-packed 75-page eBook, the Comprehensive List of Mathematical Symbols will take you through thousands of symbols in 10+ topics and 6 main categories. Each symbol also comes with their own defining examples, LaTeX codes and links to additional resources, making the eBook both a handy reference and a powerful tool for consolidating one's foundation of mathematics. Highlights - Featuring 1000+ of symbols from basic math, algebra, logic, set theory to calculus, analysis, probability and statistics - Comes with LaTeX code, defining contextual examples and links to additional resources - Clear. Concise. Straight-to-the-point with no fluff. - Informative. Engaging. Excellent for shortening the learning/reviewing curve. Table of Contents 1) Constants Key Mathematical Numbers Key Mathematical Sets Key Mathematical Infinities Other Key Mathematical Objects 2) Variables Variables for Numbers Variables in Geometry Variables in Logic Variables in Set Theory Variables in Linear/Abstract Algebra Variables in Probability and Statistics Variables in Calculus 3) Delimiters Common Delimiters Other Delimiters 4) Alphabet Letters Greek Letters Used in Mathematics Other Greek Letters 5) Operators Common Operators Number-related Operators Common Number-based Operators Complex-number-based Operators Function-related Operators Common Function-based Operators Elementary Functions Key Calculus-related Functions and Transforms Other Key Functions Operators in Geometry Operators in Logic Logical Connectives Quantifiers Substitution/Valuation-based Operators Set-related Operators Operators in Algebra Vector-related Operators Matrix-related Operators Vector-space-related Operators Abstract-algebra-related Operators Operators in Probability and Statistics Combinatorial Operators Probability-related Operators Probability-related Functions Discrete Probability Distributions Continuous Probability Distributions and Associated Functions Statistical Operators Operators in Calculus Operators Related to Sequence, Series and Limit Derivative-based Operators Integral-based Operators 6) Relational Symbols Equality-based Relational Symbols Comparison-based Relational Symbols Number-related Relational Symbols Relational Symbols in Geometry Relational Symbols in Logic Set-related Relational Symbols Relational Symbols in Abstract Algebra Relational Symbols in Probability and Statistics Relational Symbols in Calculus 7) Notational Symbols Common Notational Symbols Intervals Notational Symbols in Geometry and Trigonometry Notational Symbols in Probability and Statistics Notational Symbols in Calculus

Discovering Higher Mathematics

Author: Alan Levine

Publisher: Academic Press

Published: 1999-10-29

Total Pages: 196

ISBN-13: 9780124454606

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Funded by a National Science Foundation grant, Discovering Higher Mathematics emphasizes four main themes that are essential components of higher mathematics: experimentation, conjecture, proof, and generalization. The text is intended for use in bridge or transition courses designed to prepare students for the abstraction of higher mathematics. Students in these courses have normally completed the calculus sequence and are planning to take advanced mathematics courses such as algebra, analysis and topology. The transition course is taken to prepare students for these courses by introducing them to the processes of conjecture and proof concepts which are typically not emphasized in calculus, but are critical components of advanced courses. * Constructed around four key themes: Experimentation, Conjecture, Proof, and Generalization * Guidelines for effective mathematical thinking, covering a variety of interrelated topics * Numerous problems and exercises designed to reinforce the key themes