Math 252
Transition to Higher Mathematics
Lecture 1
Introduction
Robb T. Koether
Hampden-Sydney College
Wed, Jan 13, 2016
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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Outline
1
Introduction
2
Assignment
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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Outline
1
Introduction
2
Assignment
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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In mathematics, what does it mean to “solve a problem?”
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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In mathematics, what does it mean to “solve a problem?”
What does it take to solve
x 2 − 100x + 9831 = 0
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
4/7
In mathematics, what does it mean to “solve a problem?”
What does it take to solve
x 2 − 100x + 9831 = 0
What does it take to solve
x8 − 1 = 0
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
4/7
In mathematics, what does it mean to “solve a problem?”
What does it take to solve
x 2 − 100x + 9831 = 0
What does it take to solve
x8 − 1 = 0
How would you justify your solution?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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What does it take to show that
x 4 − 4x 3 + 6x 2 − 4x + 2 = 0
has no solution in real numbers?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
5/7
What does it take to show that
x 4 − 4x 3 + 6x 2 − 4x + 2 = 0
has no solution in real numbers?
What does it take to show that the sum of two even integers is an
even integer?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
5/7
What does it take to show that
x 4 − 4x 3 + 6x 2 − 4x + 2 = 0
has no solution in real numbers?
What does it take to show that the sum of two even integers is an
even integer?
What does it take to show that every positive integer can be
factored into primes?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
5/7
What does it take to show that
x 4 − 4x 3 + 6x 2 − 4x + 2 = 0
has no solution in real numbers?
What does it take to show that the sum of two even integers is an
even integer?
What does it take to show that every positive integer can be
factored into primes?
What does it take to show that if a set has n elements, then it has
more than n subsets, but does not necessarily have more than 2n
subsets?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
5/7
What does it take to show that
x 4 − 4x 3 + 6x 2 − 4x + 2 = 0
has no solution in real numbers?
What does it take to show that the sum of two even integers is an
even integer?
What does it take to show that every positive integer can be
factored into primes?
What does it take to show that if a set has n elements, then it has
more than n subsets, but does not necessarily have more than 2n
subsets?
How would you justify your answers?
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
5/7
Outline
1
Introduction
2
Assignment
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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Assignment
Homework
Read Chapter 0.
Read Chapter 1 through Theorem 1.11 and give it some thought.
Robb T. Koether (Hampden-Sydney College) Math 252Transition to Higher Mathematics
Wed, Jan 13, 2016
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