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 forMon Aug 24 (Solutions) (5) You are welcome to state "not finite" as "infinite". Although, "not finite" would work just as well. HW forWed Aug 26 (Solutions) (3) If a statement and its converse are true, this is when we use the language "if and only if". HW forFri 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 forMon 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 forFri 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 forWed 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 forFri 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 forMon 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 forWed Sep 16 (Solutions) (1) Add the numbers, then reduce mod 6. (3) Note we are reducing mod 8. Email Q&A HW forFri 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 forMon 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 forWed 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 forFri 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 forMon 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 forWed 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 forFri 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 forWed 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 forMon 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 forWed 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 forMon 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 forWed 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 forFri Nov 6 (Solutions) (1) The picture tells the story. (3) Greek prefixes on # of faces. HW forMon Nov 9 (Solutions) (1) Check out the vertices? (2) Face shape(s)? (3) Total angle measure in four squares? HW forWed Nov 11 (Solutions) (2) Use can use F-E+V=2 to get one once you know the other two. HW forMon 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 forWed Nov 18 (Solutions) (2) Diagonal of a rectangle? (3) Diagonal of a rectangular solid? HW forFri 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) 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