Math 300, Transition to Advanced Mathematics
Prof. Adela Vraciu
oce: LeConte 300H; email: [email protected]
Oce Hours: Tuesday and Thursday 23:30, or by appointment.
Prerequisites: Math 142.
Textbook: How to read and do proofs, by D
1. Consider the statement: For every integer x there is an integer y such that x + y is an
a. Write the above statement symbolically using quantiers.
Answer: (x)(y)(x + y is odd) (universe= all integers)
b. Give a pr
1. Give the truth value of each of the following propositions. Give a brief justication
for each answer.
a. Either 3 + is a rational number or 4 > 0.
Answer: This has the form p q where p is F and q is T, so p q is T.
b. It is no
1. Use Rolles theorem to show that x3 + 5x 2 = 0 does not have more than one real
Rolles theorem says that if y = f (x) is a dierentiable function, and x1 < x2 are real
numbers such that f (x1 ) = f (x2 ) = 0, then ther