Due Date	Homework from the textbook (partial solutions)	Preparation for Certification Exam (partial solutions)	Questions for Out of Class	Class Projects
9/2	p. 203: 19(a-c) p. 214: 16, 18 p. 243: 2, 3, 6, 9, 10, 19(a)	Certification Review #1 due For this and all future reviews, you can choose which 5 exercises to do. Please submit a total of 5 exercises only; the grader will be instructed to only grade the first 5 solutions that are submitted. Warning: If a problem looks too easy to be true, it might not be. So be careful and check for subtleties. At the top of your write-up, you must also write a statement attesting that you have at least thought about all assigned problems. Points will be deducted if you do not write this statement. (This does not mean that you solved all of the problems --- just that you gave some thought about how to solve every problem.)	None. All presentations will be peer-graded.	Topics for the class project will be assigned on a first-come, first-served basis. Please sign up by e-mail, suggesting about 5-10 different topics (in priority order) in case your first choice is no longer available. You are welcome to request all four topics for the whole semester if you wish, or you can request your topics one at a time. Be sure to title your file in the form John_Doe_15.docx, as indicated in the instructions.
9/9	p. 244: 20, 22, 33, 37, 43, 48, 51 Hints: #22: Ignore the part about the Euclidean algorithm since we didn’t cover that in class. Just get the answers. #33: It’s false. So you just need to find one counterexample. #48: Argue by contradiction. Suppose that p is a prime that divides bd. Show that p can’t divide ad+bc. FYI: This theorem is a follow-up to p. 203 19(a-c) from last week.	Certification Review #2 due		Part 1 (Pre-Algebra and Probability/Statistics) is due. The project should be submitted through Blackboard.
9/16	p. 244: 25, 30, 31, 32 p. 251: 3, 4, 5, 6, 10, 15, 16 Hints: #31: Of course, 12 = 2^2 * 3 and 120 = 2^3 * 3 * 5. So how much flexibility does that give you with the prime factorization of x? #32: Try x = 10p, where p is a prime greater than or equal to 7.	Certification Review #3 due	Group 1: Monday, 9/12 10-10:50 in GAB 473, Questions 1-10. Group 2: Tuesday, 9/13 12:40-1:30 in GAB 461, Questions 11-20. Group 3: Wednesday, 9/14 10-10:50 in GAB 473, Questions 21-30. Group 4: Friday, 9/16 10-10:50 in GAB 473, Questions 31-40.
9/23	p. 253: 2, 4, 6, 9 p. 254: Let’s Go 4 p. 263: 10, 31 Hints: p. 253 #9: Remember that to show a proposition is false, you only need one counterexample. p. 263 #31: I’m not looking for a formal proof; finding acceptable values of y via trial-and-error is perfectly fine. Problem 4.1: Here's a popular magic trick for children: (a) Take any 3-digit number in which the first and last digits differ by 2 or more. (b) Reverse the number, and subtract the smaller of the two numbers from the larger (e.g. 782-287=495). (c) Then reverse the result and add (thus 495+594=1089). Prove that you always end up with 1089. Problem 4.2: (a) Here's a second magic trick. Cut out the six numbered cards, read the instructions, and perform this trick (either by yourself or for a friend). Write a statement attesting that you actually did do this. (b) Use binary numbers to explain why this magic trick works. Hint: Find the binary representation of the first few numbers on each of the six cards. Do you see a pattern?	Certification Review #4 due		Part 2 (Algebra I and Algebra II) is due. The project should be submitted through Blackboard.
9/30	EXAM #1 on Wednesday, 9/28 in Sage Hall Testing Center, located in Suite C330. I will be at the Testing Center between 8-10:50. You may arrive at any time between 8 and 9, and you will have 1 hour, 50 minutes from the time of your arrival to complete the exam. Please talk to Dr. Q to make alternate arrangements if you’re not able to block off 1 hour, 50 minutes on this morning. The review questions should help prepare you for the exam. There are also solutions for the review questions; I encourage you to watch these videos only after attempting the review questions for yourself. Also, I don’t claim infallibility. If you think I made an inadvertent mistake while recording these videos, please let me know so I can take a look at it. No homework from the textbook will be due on 9/30.	Certification Review #5 due
10/7	p. 254: Let’s Go 3 p. 264: 18, 19, 20(a-d), 23, 24, 26, 27, 28, 33(a)	Certification Review #6 due	Group 1: Monday, 10/3 10-10:50 in GAB 473, Questions 41-50. Group 2: Tuesday, 10/4 12:40-1:30 in GAB 461, Questions 51-60. Group 3: Wednesday, 10/5 10-10:50 in GAB 473, Questions 61-70. Group 4: Friday, 10/7 10-10:50 in GAB 473, Questions 71-80.
10/14	p. 229: 2, 3(cd), 5, 6, 7, 8 p. 347: 2, 5 Notes: p. 230 #2 and #3: Your answers should have the form (something) + (something else) i. Also, your answer for #2 should match the answer to #3(a) if a = 3 and b = 2. p. 230 #6 and #7, the expressions were given in class and in the class notes. You need to prove that these expressions are true. Don't just state them without proof. Regarding p. 347 #2 and #5: We will not cover Section 12.1 in class. So I just expect you to (1) experiment with a graphing calculator until you find cubic polynomials that meet the given criteria, and then (2) once you have your polynomial, then you should explain why it meets the given criteria. You may need to use factoring and/or calculus to produce an adequate explanation. (It is possible to construct such polynomials more systematically, and you are welcome to try to find out how to do these problems without blindly guessing.)	Certification Review #7 due		Part 3 (Geometry) is due. If you haven't selected a question from all five areas yet, I encourage you to select questions from the remaining area(s) for this week's submission.
10/21	p. 347 #8(ab), 9 pp. 348-350 Your Turn 12(a), 14(a) p. 353 #1, 2, 4, 10 Hints: p. 347 #8, the local extrema and point of inflection are found by solving f '(x) = 0 and f ''(x) = 0, respectively. Then verify that the x-coordinate of the point of inflection is the average of the x-coordinates of the two local extrema. p. 348 Your Turn 12(a): Do not use the Conjugate Root Theorem (although your answer should match what you’d expect from the Conjugate Root Theorem). Instead, begin by multiplying out (x – 5 – 3i)(x –a – bi). Then collect the constant terms, the terms containing x, and the terms containing x^2. Then figure out the values of a and b so that the imaginary part of this product is equal to zero. p. 353 #10, find both the possible number of positive roots and the possible number of negative roots.	Certification Review #8 due	Group 1: Monday, 10/17 10-10:50 in GAB 473, Questions 81-90. Group 2: Tuesday, 10/18 in GAB 461 12:40-1:30, Questions 91-100. Group 3: Wednesday, 10/19 10-10:50 in GAB 473, Questions 101-110. Group 4: Friday, 10/21 10-10:50 in GAB 473, Questions 111-120.
10/28	EXAM #2 on Wednesday, 10/26 in Sage 154 (this is a change). I will be in the room between 8-10:50. You may arrive at any time between 8 and 9, and you will have 1 hour, 50 minutes from the time of your arrival to complete the exam. Please talk to Dr. Q to make alternate arrangements if you’re not able to block off 1 hour, 50 minutes on this morning. The review questions should help prepare you for the exam. There are also solutions for the review questions; I encourage you to watch these videos only after attempting the review questions for yourself.	Certification Review #9 due
11/4	p. 266: Your Turn 34 p. 269: 1, 3(bc), 4 p. 347: 6 p. 353: 5 p. 365: 2, 3(a), 7(bcde) Notes: For p. 269 #4, let the following guide your thinking: You can easily check that x = 2 is a root of f(x) = x^3 + 4x^2 – 2x – 20 and that x = -2 is a root of g(x) = -x^3 + 4x^2 + 2x – 20. So, let f(x) = an x^n + … + a1 x + a0. If you know that f(a) = 0, is there a way to modify the coefficients of f and create a new polynomial g so that g(-a) = 0? Once you see how to do this, then you’ll need to prove that your idea actually works. Hint for p. 353 #5: Start with f(x) = x^2 – p, and argue by contradiction. For p. 365 #2(c), it may also be helpful to also graph the polynomial (with a calculator) on the interval [-2,3]. Hint for p. 366 #7(e): (1+a)(1-a+a^2) = 1+a^3.	Certification Review #10 due
11/11	p. 277 Your Turn 1 p. 278: 2, 3, 11, 12 p. 280: Your Turn 5(eg) p. 280: 1(a-d) p. 284: 3, 13 p. 319: 5, 7(abd)	Certification Review #11 due	Group 1: Monday, 11/7 10-10:50 in GAB 473, Questions 121-130. Group 2: Tuesday, 11/8 in GAB 461 12:40-1:30, Questions 131-140. Group 3: Wednesday, 11/9 10-10:50 in GAB 473, Questions 141-150. Group 4: Friday, 11/11 10-10:50 in GAB 473, Questions 151-160.	.
11/18	p. 288: 1, 3, 12(ab) p. 291: 3, 4, 6, 16 p. 307: 1, 2, 5(ac) p. 317: 6 For p. 307 #5(c), ignore the instruction that says "If a product is required within an exponentiation problem, compute it via logarithms." For p. 317 #6(b), you just need a value of h, not the largest value of h that meets the condition. Problem 10.1 Unfortunately, linear interpolation isn’t particularly accurate when the “gap” between successive logarithms is large. For this reason, practicing scientists and engineers of previous generations sometimes used the following estimation formula: log(z+d) = (log z) + 0.4343 d / ( z + (d/2) ), where z is a value for which log z is known and d is the correction. (a) Using the above formula, estimate log 1.094 to four decimal places. Use z = 1.09, the value of log(1.09) from the table of logarithms, and d = 0.004. (b) Repeat to estimate log 1.097 to four decimal places. Use z = 1.10, the value of log(1.1) from the table of logarithms and d = -0.003. Problem 10.2 Use Taylor series to justify the above estimation formula. Hints: (a) log e ≈ 0.4343. (b) Use two of the Laws of Logarithms to get a single natural logarithm on the left-hand side. (c) Let t = d/z, and find the the first three terms of the Taylor series expansion of the left-hand side using the formula for the expansion of ln(1+x). (d) On the right-hand side, again let t = d/z (so that z = d/t), and rearrange so that it has the form t * 1/(1 + something). Then use the Taylor series expansion of 1/(1+x) to find the first three terms of the Taylor series expansion of the right-hand side. (e) You should find that the first two terms of the two expansions are the same, while the third term is only slightly different.	Certification Review #12 due		Part 4 (Precalculus) is due. Be sure that you’ve selected a question from all five areas.
Wednesday, 11/23	p. 129: 6, 7, 8 p. 231: 15, 23(abde), 25 p. 328: 4, 6 Notes: For p. 231 #23(de), only answer the parts involving 1-i. For p. 328 #6, be sure to consult Section 9.3.1 (pp. 281-283) before answering.	Certification Review #13 due	Re-Do Session: Monday, 11/21 10-10:50 in GAB 473, Questions 171-185. The score on the re-do will replace the lowest of the four presentation grades. So, if your presentation grades are three 100s and a 99, you probably don’t want a re-do. Non-participants are still welcome to attend and watch the re-do session. Students in the Tuesday group who’d like a re-do should schedule an appointment with Dr. Q.
12/2	EXAM #3 on Friday, 12/2 in Sage 154 (this is a change). I will be in the room between 8-10:50. You may arrive at any time between 8 and 9, and you will have 1 hour, 50 minutes from the time of your arrival to complete the exam. Please talk to Dr. Q to make alternate arrangements if you’re not able to block off 1 hour, 50 minutes on this morning. The review questions should help prepare you for the exam. There are also solutions for the review questions; I encourage you to watch these videos only after attempting the review questions for yourself.	Certification Review #14 due
Thursday, 12/8 Due by noon in Dr. Q’s mailbox in GAB 435 (Feel free to bring these to class on 12/7)	p. 328: 8, 9 p. 334: 1, 2, 3, 4(b), 6(bc), 8 p. 337: 1	Certification Review #15 due	You can also submit the optional course survey and one copy of the consent form at any time up to and including the date of the final. These surveys and consent forms were distributed in class on Monday, November 28. Completion of the survey is worth an extra 100 on both the homework problems and the certification review problems.
Wednesday, 12/14 8:00-10:00	The review questions should help prepare you for the final. There are also solutions for the review questions; I encourage you to watch these videos only after attempting the review questions for yourself.