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The Definitive Guide to Learning Higher Mathematics — 10 Principles to Mathematical Transcendence
A comprehensive, 10-chapter, illustrated guide on optimizing higher mathematical learning. Tailored towards aspiring mathematicians and higher math enthusiasts, it uncovers how one can learn math faster, more efficiently and in a more meaningful way through 10 foundational learning principles and numerous actionable, contextualized tips.
For more, see http://mathvault.ca/higher-math-learn...
== Table of Contents ==
0) Preface
1) Choose Your Materials Judiciously
1.1) Great Materials Put You in the Proximal Zone
1.2) Great Materials are Well-Structured and Standalone
1.3) Your Best Materials Evolve Over Time
2) Always Keep the Big Picture in Mind
2.1) Getting the Big Picture Through Thinking
2.2) Getting the Big Picture Through Good Habits
3) Operate Within the Proximal Zone
3.1) Prioritize on Solving Marginally Challenging Problems
3.2) Keep Your Mental Processes in the Proximal Zone
3.3) Use Effective Learning Habits to Tap into the Proximal Zone
4) Isolate Until Mastered Before Moving On
4.1) Find Your Weaknesses and Tackle Them Upfront
4.2) Cognitive Techniques Matter
4.2.1) The Power of Representations
4.2.2) The Power of Chunking
4.2.3) The Power of Bridging
4.2.4) The Power of Dynamic Repetition
5) Be a Proactive, Independent Thinking and Learner
5.1) Active Learning vs. Receptive Learning
5.2) Proactive Learning Trumps Them All
5.3) Proactive Problem-Solving in Action
6) Do Most Things Inside Your Head
6.1) The Hidden Cost of Outsourcing Our Brain to Technologies
6.2) Tips on Maximizing the Use of One's Mathematical Faculty
7) Practice the Scientific Method in a Creative Way
7.1) The Scientific and Aesthetic Nature of Mathematics
7.2) Making Mathematical Learning Both Creative and Scientific
8) Don't Fret Too Much About Real-life Applicability
8.1) The Potential Danger of Applicability-Driven Learning
8.2) The Duality Between Pure and Applied Mathematics
9) Scale Up Learning By Going Social
9.1) The Benefits of Group Learning in Mathematics
9.2) Incorporating Group Learning Into Higher Mathematics
10) Embrace the Mathematical Experience
10.1) Rehumanizing Mathematics
10.2) The Role of Appreciation and Resilience in Mathematics
10.3) Revisiting Our Mathematical Experiences
11) Last Few Words
12) Index
For more, see http://mathvault.ca/higher-math-learn...
== Table of Contents ==
0) Preface
1) Choose Your Materials Judiciously
1.1) Great Materials Put You in the Proximal Zone
1.2) Great Materials are Well-Structured and Standalone
1.3) Your Best Materials Evolve Over Time
2) Always Keep the Big Picture in Mind
2.1) Getting the Big Picture Through Thinking
2.2) Getting the Big Picture Through Good Habits
3) Operate Within the Proximal Zone
3.1) Prioritize on Solving Marginally Challenging Problems
3.2) Keep Your Mental Processes in the Proximal Zone
3.3) Use Effective Learning Habits to Tap into the Proximal Zone
4) Isolate Until Mastered Before Moving On
4.1) Find Your Weaknesses and Tackle Them Upfront
4.2) Cognitive Techniques Matter
4.2.1) The Power of Representations
4.2.2) The Power of Chunking
4.2.3) The Power of Bridging
4.2.4) The Power of Dynamic Repetition
5) Be a Proactive, Independent Thinking and Learner
5.1) Active Learning vs. Receptive Learning
5.2) Proactive Learning Trumps Them All
5.3) Proactive Problem-Solving in Action
6) Do Most Things Inside Your Head
6.1) The Hidden Cost of Outsourcing Our Brain to Technologies
6.2) Tips on Maximizing the Use of One's Mathematical Faculty
7) Practice the Scientific Method in a Creative Way
7.1) The Scientific and Aesthetic Nature of Mathematics
7.2) Making Mathematical Learning Both Creative and Scientific
8) Don't Fret Too Much About Real-life Applicability
8.1) The Potential Danger of Applicability-Driven Learning
8.2) The Duality Between Pure and Applied Mathematics
9) Scale Up Learning By Going Social
9.1) The Benefits of Group Learning in Mathematics
9.2) Incorporating Group Learning Into Higher Mathematics
10) Embrace the Mathematical Experience
10.1) Rehumanizing Mathematics
10.2) The Role of Appreciation and Resilience in Mathematics
10.3) Revisiting Our Mathematical Experiences
11) Last Few Words
12) Index
86 pages, ebook
Published November 1, 2018
12 people want to read
About the author
Math Vault
5 books1 followerDigital publisher of higher mathematics. Get a healthy dose of fun math challenges with our Higher Math Proficiency Test at mathvault.ca/math-test.
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Displaying 1 of 1 review
October 1, 2019
This book offers strategies on how to develop the habits and mindset of a great problem solver. This book is not your typical math book with problem sets, and it's not intended as such.
This book is short read (60 pages); however, don't let that fool you into thinking it's a shallow book. This book is very compact, succinct, and it balances text with lots of visual examples as well.
My motivation for reading this book:
I started self-teaching myself basic mathematics again recently to prepare myself for a discrete mathematics course that I plan on taking 6-8 months from now.
My intention in reading this book was to:
- get exposure on how to think when it comes to mathematical problem solving
- develops the proper habits to help me minimize ineffective learning strategies and to maximize building effective thinking models to build a strong mathematical foundation
The truth is, I got what I was looking for and so much more.
Lastly, I want to mention 3 reasons why I believe I received so much out of this book.
1) My high-level of motivation for wanting to learn mathematics stems from how I see it connected to my work and life, in the near future.
2) I had previous exposure to the concepts described in this book from previous books I had read on the subject of "learning how to learn" over the past 2 years (listed below),
3) Over the past year, I have been surrounding myself around lots of really passionate and intelligent learners and experts who talked about these terms vaguely to me. This book formalized the general ideas I heard and crystalized them for me.
I mention these point because I believe it's a testament to well researched and thought out this book is. This book did an excellent job of condensing the great ideas of experts in the fields of learning and effective cognition.
- Peak by Anders Ericsson (creator of 10,000 hour rule & researcher who has studied the top athletes and mental performers across almost every domain imaginable)
- How to Solve It by Mathematician George Polya.
- Exposure to Richard Feynman's video lectures on learning
- Exposure to Cal Newport's work (Deep Work, So Good they Can't Ignore You) and his other works on active learning.
Table of Contents:
1. Choose your Learning Material 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 and Independent 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
Critiques:
- I didn't agree with everything in Chapter 8, but from the perspective of higher abstract mathematics I can entertain the thought.
This book is short read (60 pages); however, don't let that fool you into thinking it's a shallow book. This book is very compact, succinct, and it balances text with lots of visual examples as well.
My motivation for reading this book:
I started self-teaching myself basic mathematics again recently to prepare myself for a discrete mathematics course that I plan on taking 6-8 months from now.
My intention in reading this book was to:
- get exposure on how to think when it comes to mathematical problem solving
- develops the proper habits to help me minimize ineffective learning strategies and to maximize building effective thinking models to build a strong mathematical foundation
The truth is, I got what I was looking for and so much more.
Lastly, I want to mention 3 reasons why I believe I received so much out of this book.
1) My high-level of motivation for wanting to learn mathematics stems from how I see it connected to my work and life, in the near future.
2) I had previous exposure to the concepts described in this book from previous books I had read on the subject of "learning how to learn" over the past 2 years (listed below),
3) Over the past year, I have been surrounding myself around lots of really passionate and intelligent learners and experts who talked about these terms vaguely to me. This book formalized the general ideas I heard and crystalized them for me.
I mention these point because I believe it's a testament to well researched and thought out this book is. This book did an excellent job of condensing the great ideas of experts in the fields of learning and effective cognition.
- Peak by Anders Ericsson (creator of 10,000 hour rule & researcher who has studied the top athletes and mental performers across almost every domain imaginable)
- How to Solve It by Mathematician George Polya.
- Exposure to Richard Feynman's video lectures on learning
- Exposure to Cal Newport's work (Deep Work, So Good they Can't Ignore You) and his other works on active learning.
Table of Contents:
1. Choose your Learning Material 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 and Independent 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
Critiques:
- I didn't agree with everything in Chapter 8, but from the perspective of higher abstract mathematics I can entertain the thought.
Displaying 1 of 1 review