Mr. Bly's Math 113 Webpage


bly@math.utk.edu


Final Exam Times
[9:05 class] Mon Dec 7 at 8am (HSS 112)
[1:25 class] Wed Dec 9 at 10:15am (HSS 53B)

Office Hours (MWF)
2:25pm-3:25pm Ayres 326




Math Tutorial Center

Ayres G012
Mon: 9am-5pm
Tue: 9am-5pm
Wed: 9am-5pm
Thu: 9am-5pm
Fri: 9am-3pm

Hodges North Commons
Sun: 5-10pm
Mon: 5-10pm
Tue: 5-10pm
Wed: 5-10pm
Thu: 6-8pm


HW Help

Test 1
HW for
Mon Aug 24
(Solutions)
(5) You are welcome to state "not finite" as "infinite". Although, "not finite" would work just as well.
HW for
Wed Aug 26
(Solutions)
(3) If a statement and its converse are true, this is when we use the language "if and only if".
HW for
Fri Aug 28
(Solutions)
(4) If p is not prime, then p must have a divisor other than 1 and p...so the sum of the divisors of a non-prime number must be strictly greater than p+1.
Email Q&A
HW for
Mon Aug 31
(Solutions)
(1) You may assume the drawer has a number of white socks and a number of orange socks.
Email Q&A
HW for
Fri Sep 4
(Solutions)
(3) Recall the classical Fibonacci sequence 1,1,2,3,5,8,... is often referred to by F_0,F_1,F_2,F_3,...
(4) Note the relation given to you essentially says the numbers T_3 and after are the sum of the three numbers prior.
Email Q&A
HW for
Wed Sep 9
(Solutions)
(2) The ratio values should be approaching the Golden Ratio (~1.62)
(3) You should not have to write out all of the thirty-plus possible compositions of 8.
HW for
Fri Sep 11
(Solutions)
(2) Either new prime you find will work for the answer.
(3) Just pick a p from among the new primes you found in 2.
Email Q&A
HW for
Mon Sep 14
(Solutions)
(2) Since we are dividing by 6, what are the possible remainders?
(4) This is a hard one to put into words. Just do your best! The hint may help you see it.
HW for
Wed Sep 16
(Solutions)
(1) Add the numbers, then reduce mod 6.
(3) Note we are reducing mod 8.
Email Q&A
HW for
Fri Sep 18
(Solutions)
(4) We need two numbers among 1,2,3,4,5 that multiply together to be a multiple of 6. Since 6 is not prime, I claim this is possible.
Test 2
HW for
Mon Sep 28
(Solutions)
(2) Factoring into primes allows you to just cancel like factors on top and bottom.
(3) Note, you just need a rational number. It need not be simplified.
HW for
Wed Sep 30
(Solutions)
(1-2) Call the number given N. Multiply N times a 1 with as many zeros after it as there are repeated decimal digits. If you subtract N from the result of the multiplication, you will get a lot of cancellation.
Email Q&A
HW for
Fri Oct 2
(Solutions)
(2) Before you bring down a 0, you have a remainder mod 7. How many such remainders are there? Eventually, the remainders have to appears again, right?
(4) What kind of infinite decimal number is M? Is there a repeating pattern or not?
Email Q&A
HW for
Mon Oct 5
(Solutions)
(3) The two examples above are practically identical to showing sqrt(p) is irrational for any p. So, any sqrt(p) is irrational. How many sqrt(p)'s are there?
HW for
Wed Oct 7
(Solutions)
(2) D having a small number of objects presents a problem when you are trying to inject C into D. One particular characteristic of injections is tough to satisfy.
HW for
Fri Oct 9
(Solutions)
(1-2) Recall two sets are in bijective correspondence if one injects into the other and the other into the one.
HW for
Wed Oct 14
(Solutions)
(1) Use diagonalization to find a*. You will have to dot dot dot after the 6th digit.
(3) This is effectively relying on the definition of uncountable.
HW for
Mon Oct 19
(Solutions)
(3) What if you count objects in R and T in an alternating fashion?
(4) How is the 100th decimal place of a* chosen?
HW for
Wed Oct 21
(Solutions)
(2) Similar to (3) of HW for Mon Oct 19.
(3) If both the irrational and rational numbers were countable, this would present a problem. How so?
Test 3
HW for
Mon Nov 2
(Solutions)
(2) What is the total measure of the two other angles which combine with the angle of interest to form a straight line?
(3) For part a., you will need to FOIL.
HW for
Wed Nov 4
(Solutions)
(2) The longest side should always be opposite the right (ie. largest) angle.
(3) a="shortest side"; b="medium side"; c="largest side".
HW for
Fri Nov 6
(Solutions)
(1) The picture tells the story.
(3) Greek prefixes on # of faces.
HW for
Mon Nov 9
(Solutions)
(1) Check out the vertices?
(2) Face shape(s)?
(3) Total angle measure in four squares?
HW for
Wed Nov 11
(Solutions)
(2) Use can use F-E+V=2 to get one once you know the other two.
HW for
Mon Nov 16
(Solutions)
(1-2) Use Pythagoras
(3-4) We showed in class the diagonal of a rectangular solid is sqrt(a^2 + b^2 + c^2).
HW for
Wed Nov 18
(Solutions)
(2) Diagonal of a rectangle?
(3) Diagonal of a rectangular solid?
HW for
Fri Nov 20
(Solutions)
(4) Repeated addition is just multiplication


Test Review Materials

Test 1
(Solutions)
Self-Quiz 8/27
Solutions
Self-Quiz 9/4
Solutions
Self-Quiz 9/11
Solutions
Self-Quiz 9/18
Solutions
Skills Checklist
Sample Test
Hints
Solutions
Test 2
(Solutions)
Self-Quiz 10/2
Solutions
Self-Quiz 10/9
Solutions
Self-Quiz 10/14
Solutions
Self-Quiz 10/21
Solutions
Skills Checklist
Sample Test
Hints
Solutions
Test 3
(Solutions)
Self-Quiz 11/6
Solutions
Self-Quiz 11/13
Solutions
Self-Quiz 11/20
Solutions
Sample Test
Hints
Solutions
Skills Checklist
Final Exam
Skills Checklist
Practice Problems
Solutions


Internet Videos

Test 1
Fri 8/21
The Converse, Inverse, and Contrapositive
Mon 8/24
If and Only If Statements
Wed 8/26
None
Fri 8/28
Pigeonhole Principle
Mon 8/31
None
Wed 9/2
The Classical Fibonacci Sequence
Fri 9/4
Fibonacci & The Golden Ratio
Wed 9/9
Expressing Whole Numbers as Products of Primes
Fri 9/11
Modular Arithmetic
Mon 9/14
None
Wed 9/16
Adding & Multiplying in Z_n (up to 7min 20sec)
Test 2
Wed 9/23
The Enigma Machine (for your enjoyment)
Fri 9/25
Rational vs. Irrational Numbers
Simplyfing Rational Numbers
Expressing Finite Decimals as Rational Numbers
Mon 9/28
Expressing Repeating Decimals as Rational Numbers
More Expressing Repeating Decimals as Rational Numbers
Wed 9/30
Rational vs. Irrational Numbers
Another on Rational vs. Irrational Numbers
Fri 10/2
Showing sqrt(2) is irrational
Mon 10/5
Cardinality & Injections (up to 6:23)
Wed 10/7
None
Fri 10/7
Cardinality of the Rational Numbers
Mon 10/12
Diagonalization and an Uncountable Infinity
Wed 10/14
Some Infinities are Larger than Others
Another Some Infinities are Larger than Others
Mon 10/19
Cantor's Hypothesis (up to 25:35; for your enjoyment)
Wed 10/21
Godel's Incompleteness Theorems
Godel (3:36 to 17:40; for your enjoyment)
Test 3
Wed 10/28
Area of a Rectangle
Distributive Property via a Rectangle
FOILing via a rectangle
Fri 10/30
A Triangle's Interior Angles
A Curious Area Problem
Mon 11/2
Acute vs. Right vs. Obtuse Triangles
Pythagorean Theorem
Wed 11/4
Platonic Solids
Fri 11/6
Duality & Platonic Solids
Mon 11/9
F - E + V = 2
Wed 11/11
None
Fri 11/13
Length of a Diagonal in a Rectangle
Length of a Diagonal in a Rectangular Solid
Mon 11/16
Distance From the Origin in the xy-plane
The xy-plane (R^2) and xyz-space (R^3)

An Image Showing How Distance in xyz-space Relates to Diagonals of Rectangular Solids
Another Such Image

Mon 11/16
Distance From the Origin in R^n


Daily Quizzes

Test 1
Fri Aug 21
Fri Aug 28
Wed Sep 2
Fri Sep 4
Wed Sep 9
Fri Sep 11
Mon Sep 14
Test 2
Fri Sep 25
Mon Sep 28
Wed Sep 30
Fri Oct 2
Mon Oct 5
Wed Oct 7
Fri Oct 9
Mon Oct 12
Wed Oct 14
Mon Oct 19
Wed Oct 21
Test 3
Fri Oct 30
Mon Nov 2
Wed Nov 4
Fri Nov 6
Mon Nov 9
Fri Nov 13
Mon Nov 16
Wed Nov 18