### Math 113 Fall 2017

Final Exams       Office Hours

8 o'clock class: Wednesday, Dec. 13 at 8:00 a.m. in Ayres 120.
9:05 class: Monday, Dec. 11 at 8:00 a.m. in Ayres 120.
If you want to switch your final exam time to the other class,
you must let me know in advance. If there is room, you may switch.

9:10 - 10:00 MWF in HSS (TBD)
1:00 - 3:00 T in 226 Ayres and by appointment.

You are welcome to drop by anytime.
If I am not busy, I'll be happy to talk to you.

#### Math Department Syllabus

Class Assignments         The homework solutions.

Please remember to do the TN Voice evaluations. I especially appreciate any comments you may have. Thanks.

#### Russian Alphabet equivalences.

The Hotel Hilbert (thanks to Jacob Z.)

The homework score will be based on a total of 250 points. The maximum possible will be 100% though. The homework is 20% of the grade.
To calculate your homework grade: Add up the three homework scores listed on your test. Also, add 10 pts. for each of the 5 group projects done and for the public key encryption - entering a key (10 pts.) and decrypting a message (10 pts.) There were over 310 total points.

#### Test 3: Friday, November 10

• Know the Pythagorean Theorem; be able to state it (in English!). Given the lengths of two sides of a right triangle find the length of the other side. Know how to tell if a triangle is a right triangle. How does the "puzzle proof" with the 4 triangles and the square show that the Pythagorean Theorem is true?
• State the Art Gallery Theorem completely accurately and in your own words and know how to apply it. Be able to choose the best-suited points to put the cameras in an art gallery. Be able to divide the museum into triangles and label the vertices. Be able to do problems like these.

Sketch a gallery with 12 vertices which needs 4 cameras or 12 vertices which needs only 3 cameras. How many cameras will you need for a gallery with 8 vertices? Can you draw a gallery with 12 vertices which needs 5 cameras? Why or why not?

• Sketch a Golden Rectangle. Given any rectangle, determine whether or not it is a Golden Rectangle. What happens if you start with a Golden Rectangle and remove the largest square from it? Given the base (long side) of a Golden Rectangle, find its height (short side). Given the height (short side) of a Golden Rectangle, find its base (long side). Be able to find the area of a Golden Rectangle given either its base or its height. Be able to draw the Golden Spiral and find its center.
• Understand tessellations, symmetry, rigid symmetry and symmetry of scale.
• Be able to draw a triangle for the basic building block of the Pinwheel Pattern and draw supertiles of the Pinwheel Pattern from five smaller tiles. Given a diagram of the Pinwheel Pattern, outline a five-tile supertile and a 25-tile supersupertile.
• Know all about the Platonic solids - their names and various numbers of edges, vertices and faces and their duals.

Due Monday November 6.

#### Test 2: Redo

You may redo one problem from test 2 on separate paper and hande it in along with the test on Friday, October 20. You can come to office hours to pick up your test or get help.

#### Test 2: Monday, October 16.

• Know Fermat's little theorem and how it relates to raising numbers to high powers in modular arithmetic.
• Know public key encryption
• Understand the various sets of numbers and their properties.
• Natural numbers, real numbers, irrational numbers, rational numbers
• Decimal expansions
• Be able to prove that a number is irrational
• Understand 1-1 correspondence and cardinality and how to show infinite sets have the same cardinality.
• Know who Georg Cantor is and how his diagonalization proof works and what it shows.

#### Test 1: Monday, September 18.

There will be about 10 problems (max)
• Be able to solve problems similar to those in chapter 1 or discussed in class.
• Be able to estimate numbers reasonably and understand and explain the pigeonhole principle.
• You should know how to find Fibbonaci numbers and their notation.
• Understand the strategy for Fibonacci nim.
• You should know what a prime number is and how to factor an integer.
• You should understand the proof that there are infinitely many prime numbers.
• Know how to compute with modular arithmetic, for example, to verify UPC codes.

Look at the suggested problems listed in the course schedules.

The problems handed out in class on the first two days.

#### Course Policies

Text: The Heart of Mathematics, by Burger and Starbird (4th edition. We will roughly cover chapters one through four with some additional topics. There is an ebook available. See the book's web page.

Tests: There will be three hour tests, plus a comprehensive final exam.

Homework and In-class assignments: There will be about 15 assignments to be handed in throughout the term. You may collaborate on problems, but must write up your own solutions. It is important to keep up with the assignments. The best way to learn math is to struggle with lots of problems. There will also be some assignments done and handed in during class. Not all of the available points will be counted, so anyone who works faithfully at them will get a good assignments grade.

Class assignments.

Grades: The 3 tests, the assignments and the final exam will each count 20% of the grade. Grades will be computed on the math departments scale: 90-100% A, 87 - 89% A-, 83 - 86 B+, 80-82% B, 77 - 79% B-, etc. Some consideration will be given to steady improvement throughout the term; of course consideration will also be given to a steady decline throughout the term.

Calculator: You should have a scientific calculator for this course. For example, any TI graphing calculator (the TI - 81 through 86) or Sharp or Casio is fine. Any calculator with an exponentiation key is fine, but not one built into your phone or with an internet connection. You will always be allowed to use a calculator on tests. If you don't have one, find the nearest pawn shop.

Make Up Policy: If you must miss due to a university sanctioned meeting let me know ahead of time. If you have an emergency, please notify me as soon as possible (email is best) to schedule a make-up.

Last update: December 31, 2018, 12:26 pm