Exam Contents

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This page lists the knowledge and skills which are "fair game" for testing on exams.

Note: This page is a work in progress. We are now adding material for the second exam.

Contents 1 Items to Memorize 1.1 Rules of Thumb 1.2 Equations 1.3 Numbers 2 Skills (Things you must be able to do)

[edit] Items to Memorize

[edit] Rules of Thumb

1. The shortest time between two events is measured in the frame where those events are separated by the smallest distance.
2. The measured length of an object will be longest in the frame where the object is at rest.

[edit] Equations

Note: For all equations, you should be able to write the equation and unpack what it means. That is, you must translate the mathematical shorthand into everyday words and explain the situations where the equation applies.

1. The Pythagorean Theorem
2. The equation for the distance between two points
3. Equations for the area of triangles and parallelograms
4. The equation which relates distance, time, and speed
5. The equation for the invariant spacetime interval
6. The equation for the time stretch factor

[edit] Numbers

1. The sum of the angles of a triangle
2. The number of meters in a kilometer (or the number of kilometers in a meter)
3. The number of centimeters in a meter (or the number of meters in a centimeter)
4. The number of meters (or kilometers) in a second (or the speed of light expressed in meters per second or kilometers per second)

[edit] Skills (Things you must be able to do)

1. Use each of the equations listed above to solve problems related to physical situations or relativistic thought experiments
2. Measure angles with a protractor
3. Determine the coordinates of points in a two-dimensional, rectangular coordinate system and write the coordinates in the conventional way
4. Measure lengths with a ruler
5. Convert lengths measured in meters to units of kilometers or centimeters
6. Use length units to answer questions about time and time units to answer questions about length
7. Explain the differences between and among the principles of relativity: "full" relativity, Galilean relativity, and special relativity (Note: This includes the ability to explain the term "uniform motion.")
8. Complete a variety of simple geometric proofs by using different combinations of the following items from Euclid's Elements
   1. definitions, postulates, and common notions
   2. propositions 1, A, B, and C (or 1, 9, 10, and 11 from Book I) -- each of which you should be able to prove as well as use
   3. congruence theorems (side-angle-side, side-side-side, and angle-side-angle)
   4. vertical and corresponding angles
9. Explain, in your own words, the differences between knowledge gained through measurement and knowledge gained through deductive proof
10. Explain, in your own words, evidence which supports the theory of special relativity
11. Show whether or not statements are paradoxical by investigating both sides of the proposed paradox
12. Explain and use the concept of a "well-defined set"
13. Explain, in your own words, the development and downfall of the various attempts to make mathematics consistent and complete: Euclidean geometry to non-Euclidean geometry to set theory to Goedel