## We Promise to Make your Math Frustrations Go Away!

Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# MATH 100 SECTION 1 SECOND BLOCK: CORE MATERIAL

BASIC CONCEPTS: apportionment and voting. For a list of basic concepts
see the lists of “Key Concepts” for Chapters 1 and 4 of Tannenbaum (on pages
29 and 144). You are not of course responsible for the material in section 1.6
on ranking (so you can ignore the key concepts on page 29 that have the word
“ranking” in them).
BASIC CONCEPTS: rational and irrational numbers.
rational number, irrational number, repeating decimal, nonrepeating decimal,
even and odd integers, right triangles
BASIC FACTS

1. The fundamental theorem of arithmetic (= the unique factorization theorem):
Every composite number can be written as a product of primes in
exactly one way (except for the order of the factors).

2. the Pythagorean theorem (page 58 of Stein)

3. theorems 1, 3, 4, 5, 6 on pages 63–66 of Stein

4. the rationality or irrationality of sums and products of rational and irrational
numbers

5. a product of odd integers is odd (so if a product of integers is even, then
at least one must be even)

6. For any natural number N, we have 7. In an election with N alternatives, the total number of pairwise comparisons
is .

8. with t candidates the number of distinct possible preference ballots is
t! = 1 × 2 × 3 × · · · × t

9. The Arrow impossibility theorem

10. the Balinski and Young impossibility theorem

11. history of apportionment in the house of representatives

SOME BASIC COMPUTATIONS

Finding the decimal form of a rational number and writing a repeating decimal
as a quotient of integers.