This page is an homage to the great theorist and Nobel laureate Gerard t'Hooft (see his web page for where this all started).

I have been looking over Gerard t'Hooft's web page for several years. Something has been bothering me about it. It is not his selection of things, but more their ordering that bothers me. Of course, he is a professional and I am an amateur; perhaps that is the problem—he did things the traditional way and I didn't, that gives me at least one case where a system of self-instruction worked. I will present that below.

Instead of listing resources solely on the web, I will include purchased items if they are very good.

If you follow these fairly carefully, you will do well.

Begin a notebook and on the first page you intend to use, write page 1 and begin. Use the techniques from Skills for Learning from the self-study course as a guide. With each topic from the list write a brief description and give at least one example. If you think something is important, even if you know it, write that down, too. You must be completely honest with yourself; if you do not understand something or its properties stop and make a detailed study of it. Some places you will be able to proceed quickly, others will take a frustratingly long time to complete.

Here is an overview of the methods you should use:

The first step is to acquire strong study skills. These will only be mastered with practice.

- Every time you encounter a new word attempt to define it. Guess it if you have to. Avoid being misled by technical terms that you think you understand. Do not expect your definition to be correct the first time. Come back to it as you learn more and refine the definition from ever more sophisticated viewpoints.
- Every time you encounter a fact or an idea ask yourself, "What is the justification of that idea? Why should you believe it? What is the proof of it, if there is any? If the idea is conjecture, what is the justification for it? How do we know this to be true?
- When you encounter an idea try to figure out how it relates to other similar ideas you have encountered. How is it similar? How is it different?
- When you encounter an idea or fact, can you tell if it is based on some observation of reality? Or is it based on inference from other ideas?
- When you encounter an idea or an argument, can you determine their underlying assumptions?
- When you encounter an idea is it the result of applying a specific idea to more general situations? Such an application is called induction. Or is it a case where general ideas are applied to specific situations? This type of application is called deduction.
- Given that certain facts will be established in the course of your study, make some predictions by applying what you have learned to situations not covered by your study so far. What do you predict will happen in these situations? Can you verify these predictions?
- Inevitably you will encounter gaps in your available information. This is true in school, and it is especially true in self-study. You will certainly encounter a situation where a fact or idea is put forward without complete information. This should not become a roadblock! To settle such occurances we note our ignorance and make an assumption that temporarily settles the matter until we can get back to it. So, when we encounter such confused issues do two things: first, make a note of the ambiguity that you are encountering; and second; determine what information or assumption on your part needs to be provided to settle it; and move on.
- In doing science we try to understand nature. The first step in this is to remove all complications and treat the object of study in the most simple and abstract way possible. Then we explore this idealized idea until we think we understand it. Beginning with such idealized and oversimplified ideas can you slowly add levels of complexity and reality until you develop your ideas into deep levels of understanding?

You will want to study the basic mathematics and mechanics at the same time.

For what follows the following are good resources:

**US Navy Training Manual, Mathematics, Basic Math and Algebra**, search for NAVEDTRA 14139 in your search engine.**US Navy Training Manual. Mathematics, Trigonometry**, search for NAVEDTRA 14140 in your search engine.**US Navy Training Manual. Mathematics, Pre-Calculus and Introduction to Probability**, search for NAVEDTRA 14141 in your search engine.**US Navy Training Manual. Mathematics, Introduction to Statistics, Number Systems and Boolean Algebra**, search for NAVEDTRA 14142 in your search engine.- David A. Santos, (2008),
**Andragogic Propaedeutic Mathematics**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-a-course-in-arithmetic.pdf. This book does not cover complex numbers, but it does have an introduction to sets. - David A. Santos, (2008),
**Ossifrage and Algebra**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-elementary_algebra_book.pdf. This book does not cover complex numbers. - David A. Santos, (2008),
**Precalculus**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-precalculus.pdf. - David Santos, (2008),
**The Elements of Infinitesimal Calculus**. This is a free download for the website: http://www.opensourcemath.org/books/santos/santos-very-basic-calculus.pdf - S. K. Chung, (2007),
**Understanding Basic Calculus**. This is a free download from the website: http://www.mathdb.org/basic_calculus/BasicCalculus.pdf - David Guichard, (2012),
**Calculus Early Transcendentals**. This is a free download from the website: http://www.whitman.edu/mathematics/multivariable/ - Wilfrid Kaplan and Donal J. Lewis, (),
**Calculus and Linear Algebra, vol.s 1 and 2**. These are a free download from the website: http://quod.lib.umich.edu/s/spobooks/. I strongly recommend these. - Dan Sloughter, (2000),
**Difference Equations to Differential Equations**, as a free download located here: http://synechism.org/drupal/de2de/.

If you wish to buy a book, I recommend Biman
Das, (2005), **Mathematics for Physics with Calculus**, Pearson Prentice Hall. The only problem
with this book is that it doesn't cover any
linear algebra.

You should be comfortable with the following before you start studying mechanics:

- Elementary set theory.
- The number system.
- Addition, subtraction, multiplication, division, exponents, roots, and logarithms for real numbers and fractions.
- Percentages.
- Measurement.
- Algebraic manipulation.
- Factoring polynomials.
- Solving linear equations.
- Ratio and proportion.
- Functions.
- Complex number arithmetic.
- Quadratic equations.
- Inequalities.
- Polynomial functions.
- Rational functions.
- Algebraic functions.
- Plane geometry.
- Geometric constructions.
- Solid figures.
- Trigonometric functions.
- Exponential functions.
- Logarithmic functions.
- Trigonometric identities.
- Vector algebra and geometry.
- Straight lines.
- Planes.
- The graphs of functions and their transformations.
- Conic sections.
- Tangents, normals, and slopes of curves.
- Limits.
- Derivatives.
- The rules of differentiation.
- Curve sketching.
- Maxima and minima problems.
- Indefinite integrals.
- Definite integrals and the fundamental theorem of calculus.
- Integration methods.
- Area.
- Volume.
- Polar coordinates.
- Parametric equations.
- First-order differential equations.
- Sequences and series.
- Matrices and determinants.

Here are other important topics to study while studying mechanics:

- Combinations.
- Permutations.
- Probability.
- Mathematical induction.
- The binomial theorem.
- Descriptive statistics.
- Boolean algebra.
- Vector functions.
- Partial differentiation.
- Multiple integrals.
- Vector calculus.
- Vector spaces.
- Linear Euclidean geometry.
- Higher-order differential equations.

You will want to study the basic mathematics and mechanics at the same time. Here are some good resources:

- Richard Fitzpatrick, (2006),
**Classical Mechanics An Introductory Course**. This is a free download from the website: http://farside.ph.utexas.edu/teaching/301/301.pdf - Richard Fitzpatrick, (2011),
**Newtonian Dynamics**. This is a free download from the website: http://farside.ph.utexas.edu/teaching/336k/336k.html - James Nearing, (2010),
**Classical Mechanics**. This is a free download from the website: http://www.physics.miami.edu/nearing/class/340/book/ - Robert E. Hunt, (2007),
**Dynamics**. This is a free download from the website: http://www.damtp.cam.ac.uk/user/reh10/lectures/

You might also want to purchase the book I am writing with famed theoretical physicist Leonard Susskind, from Stanford University. This book has a planned release date of January of 2013:

- Leonard Susskind, George Hrabovsky, (2013),
**Theoretical Minimum Classical Mechanics**, Basic Books.

Here are the concepts you need to master:

- Dimensional analysis and estimation.
- Kinematics in one dimension.
- Differentiation and integration of vector functions of a single variable.
- Kinematics in more than one dimension.
- Newton's law of motion.
- Differential equations with constant coefficients.
- Solving Newton's equations of motion for time-dependent forces.
- Series solutions of differential equations.
- Numerical solution of differential equations.
- Solving Newton's equations of motion for velocity-dependent forces.
- Parametric curves.
- Line itnegrals.
- Work, power, and kinetic energy.
- Scalar and vector fields.
- The gradient of a scalar field.
- Potential energy and force.
- Solving Newton's equations of motion for position-dependent forces.
- Conservation of energy.
- Energy diagrams.
- Conservation of momentum.
- Conservation of angular momentum.
- Systems of particles and center of mass.
- Collisions.
- Rigid bodies.
- Statics of rigid bodies.
- Kinematics of rigid bodies.
- Damped oscillators.
- Phase space techniques.
- Forced oscillators and resonance.
- Fourier series.
- Green's functions.
- Coupled oscillators.
- Waves on a string.
- Perturbation theory.
- Central forces.
- Orbits.
- The two-body problem.
- Scattering.
- Galilean relativity.
- Motion in a rotating frame.
- Tides.
- Moment of inertia.
- Energy, momentum, and angular momentum of a rigid body.
- Kinematics of simple harmonic oscillators.
- Dynamics of simple harmonic oscillators.
- Energy, momentum, and angular momentum of simple harmonic oscillators.
- Generalized coordinates.
- The principle of least action.
- Lagrange's equations of motion.
- The calculus of variations.
- Constraints.
- Hamilton's equations of motion.
- Legendre transforms.
- Gravitational potentials.
- The three-body problem.
- Chaos theory.
- Poisson brackets.
- Canonical transformations.
- Particles in electric and magnetic fields.

Here are the concepts you should be familiar with:

- Variable mass problems (like rockets).
- Circular motion.
- Statics.
- The inertia tensor and rigid body rotations.
- Particles in electromagnetic fields.

Here are some topics you might become interested in:

- The Earth-Moon system.

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