How to Solve A Problem

Table of contents

1. Cover
2. Endorsements
3. Half Title
4. Title
5. Copyright
6. Dedication
7. Contents
8. Preface
9. Acknowledgments
10. Author Biography
11. 1 On Encountering a Problem
    1. What Is a Problem?
    2. The Right to Propose a Problem
       1. The Implicit Faculty Commitment
       2. The Responsibility of the Problem Solver
          1. The Student’s Personal Commitment
    3. Preparing for Problems
    4. Patience, Persistence, and Problem-Solving
    5. Knowing ≤ (The Battle)/2
    6. To Take on a Problem
       1. What’s Really a Blessing?
12. 2 The Logic of the Problem: Good Thinking and Its Rewards
    1. Subject-Independent Logic (Subject-Specific Laws)
    2. Scientific Laws ‘Do’ Nothing
    3. General Logical Ideas in Science
       1. The Logic of Limiting Factors
       2. The Logic of Amounts
    4. Units – The Basics
    5. Units and Meaning
    6. Logic above Memorization
    7. Reading a Chemical Formula – Not Only for Chemists
13. 3 Solutions in Words: Answering Short Answer Questions
    1. Symbols and Words
    2. Short Answers in Words
14. 4 Making Textbooks Pay
15. 5 Solutions in Numbers: Basic Mathematical Procedures
    1. Some Mathematical Reminders
       1. (1) Algebraic Manipulations and Some Useful Math Relations
       2. (2) Trigonometric Ideas
          1. Beyond Triangles
       3. (3) Other Interesting Relationships and Definitions
          1. Helpful Definitions and Quantities
    2. More Emphasis on Logarithms and Powers
    3. Linear (Straight-Line) Equations
    4. Quadratic Equations
    5. Graphical Representations of Experimental Data
    6. Simultaneous Equations
       1. Option 1 – The Exponential Form:A=Aoe-kt
       2. Option 2 – The Straight Line Form: ln(A) = ln(Ao) – kt
          1. An Extra Example
    7. A Word on Matrices
    8. On the Shapes of Things
       1. Circles, Cylinders, and Spheres
       2. Triangles and (Triangular) Prisms
       3. Rectangles and Cuboids
    9. Layer upon Layer
       1. A Fun Illustration from Shapes
       2. Stay the Course
16. 6 Practical Solutions: Science in the Laboratory
    1. Why Experiments Matter
    2. Approaching Laboratory Activities
       1. Insist on High Standards of Logic and Reasoning
       2. Be Willing to Think Independently and Take on New Challenges
       3. An Appreciation of Errors
       4. Another Suggestion to Keep in Mind
       5. The Unknown Possibilities
       6. Ethical Engagement
17. 7 Spreading the Word
    1. Preparing Papers
    2. Writing Abstracts
    3. Preparing Posters
    4. Preparing Talks
18. 8 Persisting against Problems
    1. Mindset and Anxiety about Belonging
    2. Thoughts on Managing the Demands
       1. Avoid Overcommitment
       2. Get a Calendar
       3. Sleep – Eat Well – Exercise
       4. Nurture Good Friendships
       5. Be Good to Others
       6. Remember Why You Are in College
       7. Be Gracious and Forgiving
       8. Celebrate
    3. On to the Next Problem
19. Appendix I Additional Notes on Matrices and Matrix Algebra
20. Appendix II Thinking about Vectors: Basic Notes
21. Appendix III Safe Problem-Solving
22. Index