For each conceptual goal develop at least one page of notes, for each capability come up with at least three examples.

A Note About Computer Algebra Systems: I strongly advise the purchase of Mathematica Home Edition, it is about $300 and is an important addition to any amateur scientist's toolbox. From here on I will assume that you are using Mathematica. There are free computer algebra systems that you can use.

The main topics covered here are:

- Elementary mathematics through calculus.
- Elementary physics.
- Elementary chemistry.

This is the foundational unit, and many will be able to just breeze through it. I do recommend that you take some time, though. The topics are not technically difficult, but they do form the basis of a philosophy of science, from which all of your work will be based. The stronger this foundation, the stronger will be your work.

- The scientific method.
- The nature of mathematics.

**Scientific Method**. This is a free download for the website: http://www.thechembook.com/wiki/images/5/59/Lecture_2_Scientific_Method.pdf- CK-12 Foundation, (2010),
**Chemistry**, CK-12 Flexbook. Specifically chapter 1. This is a free download from the website: www.ck12.org - Larry Woolf, (2004),
**How do scientists really do science?**This is a free download from the website: http://www.sci-ed-ga.org/pdfs/how-do-science-10-10-04.pdf - George Hrabovsky, (2009),
**There is No Scientific Method**. This is a free download from the websight: http://www.madscitech.org/guide/Theory.pdf

This unit is designed to give you a quick overview of mathematics.

Unit 1 Elementary Mathematics and Science: Introduction to Mathematics and Science, and Unit 1 Elementary Practical Science: Introduction to Doing Science, and Unit 1 Independent Study: Introduction to Studying Mathematics and Science.

- Arithmetic operations: addition, subtraction, multiplication, division, exponentiation, radicals, and logarithms.
- The basics of set theory: sets, elements, lists, set-builder notation, subsets, equal sets, the empty set, union, intersection, difference, and symmetric difference.
- The number system: natural numbers, integers, rational numbers, irrational numbers, decimals as approximations, real numbers, imaginary numbers, and complex numbers.
- Geometric ideas: points, sets of points, lines, planes, intersecting lines, angles, triangles, other polygons, circles, solid figures, area, surface area, and volume.
- Algebra: symbolic representation, algebraic expressions, equations, inequalities, representing equations and inequalities geometrically, and types of equations and inequalities.
- Functions: Cartesian products, relations, equivalence relations, functions, common algebraic functions, and representing functions geometrically.
- Calculus: Sequences, limits of sequences, limits of functions, the derivative, differentiation rules, the antiderivative, the integral, the fundamental theorem of calculus, and series.

- Perform each arithmetic operation on any two numbers.
- Represent a set in set-builder notation, including subsets, union, intersection, difference, and symmetric difference.
- Demonstrate sets using Venn diagrams: subsets, union, intersection, difference, and symmetric difference.
- Explain the idea of completeness of the number system.
- Explain how the number system evolved from natural numbers to complex numbers to gaurantee completeness.
- Be able to make diagrams of each type of geometric figure.
- Be able to calculate lengths, angles, areas, surface areas, and/or volumes for all major geometrical figures.
- Be able to convert a written statement concerning quantities into an algebraic expression.
- Be able to perform arithmetic operations on algebraic expressions.
- Be able to factor, expand, and simplify algebraic expressions as needed.
- Derive, solve, and plot the solutions of linear, rational, radical, quadratic, cubic, and quartic equations and inequalities.
- Explain Cartesian products as they relate to graphs.
- Explain relations, equivalence relations, and functions in terms of sets.
- Represent common algebraic functions as equations, tables, and Cartesian graphs. The functions include linear, polynomial, rational, exponential, and logarithmic.
- Explain sequences and convergence.
- Be able to calculate the limit of a sequence.
- Extend the idea of the limit of a sequence to a function.
- Be able to calculate the limits of functions.
- Explain the idea of a derivative, higher-order derivatives, the constant rule, the constant multiple rule, the sum rule, the power rule, the product rule, the quotient rule, and the chain rule.
- Be able to calculate the derivatives of functions.
- Explain the idea of the integral.
- Be able to calculate the integrals of functions.
- Use the fundamental theorem of calculus to calculate definite integrals.

**US Navy Training Manual, Mathematics, Basic Math and Algebra**, search for NAVEDTRA 14139 in your search engine.**US Navy Training Manual. Mathematics, Pre-Calculus and Introduction to Probability**, search for NAVEDTRA 14141 in your search engine.- David A. Santos, (2008),
**Andragogic Propaedeutic Mathematics**. This is a free download for the website: http://faculty.ccp.edu/faculty/dsantos/lecture_notes.html. 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://faculty.ccp.edu/faculty/dsantos/lecture_notes.html. This book does not cover complex numbers. - David A. Santos, (2008), Precalculus. This is a free download for the website: http://faculty.ccp.edu/faculty/dsantos/lecture_notes.html.
- CK-12 Foundation, (2010),
**Math Analysis**, CK-12 Flexbook. This is a free download from the website: www.ck12.org **HELM Workbooks (Helping Engineers Learning Mathematics)**, Available as a free download from the website: http://www.maths.sussex.ac.uk/Staff/RML/HELM/- Jerrold E. Marsden, Alan Weinstein, (1985),
**Calculus I**. Available as a free download from the website: http://caltechbook.library.caltech.edu/view/person-az/Marsden-J-E.html - CK-12 Foundation, (2010),
**Single-Variable Calculus**, CK-12 Flexbook. This is a free download from the website: www.ck12.org

This unit is designed to give you a quick overview of chemistry and physics. This is a very long unit.

Unit 2 Elementary Mathematics and Science: Mathematics, and Unit 2 Elementary Practical Science: Problem-Solving.

- Basic Science: Units of measurement, scientific notation, unit conversions, dimensional analysis
- Physics: Motion, position, displacement, velocity, mass, kinetic energy, acceleration, potential energy, the conservation of energy, momentum, the conservation of momentum.
- Particles: Newton's laws of motion, work, power, angular momentum, and the conservation of angular momentum.
- Matter: Collisions, accretion, explosions, systems of particles, center of mass, moment of inertia, rigid bodies, statics, elastic solids, fluid statics, fluid dynamics, and the zeroth, first, second, and third laws of thermodynamics.
- Chemistry: Atoms, molecules, chemical elements and isotopes, chemical formulas and equations, chemical reactions, reaction yields, kinetic theory, thermochemistry, and chemical equilibrium.

- Identify the primary SI units of length, time, mass, temperature, and current..
- Identify the derived SI units for area, volume, density.
- Given a density, find the mass or the volume.
- Use the prefixes for units from pico to mega in scientific notation.
- Be able to treat units as algebraic symbols.
- Convert from SI to cgs and English systems of units.
- Use dimensional analysis to derive formulas.

- CK-12 Foundation, (2010),
**People's Physics Book Version 2**, CK-12 Flexbook. This is a free download from the website: www.ck12.org - CK-12 Foundation, (2010),
**21st Century Physics Flexbook**, CK-12 Flexbook. This is a free download from the website: www.ck12.org - Benjamin Crowell, (2009),
**Simple Nature**. This is a free download for the website: http:// www.lightandmatter.com - CK-12 Foundation, (2010),
**Chemistry**, CK-12 Flexbook. Specifically chapter 1. This is a free download from the website: www.ck12.org

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