Basic Course Information / Links

Course Sections (click on the section number for syllabus)

Section 52037 / 52038: MTWRF 9:15am-10:15am in Boyd 323

 

Useful Website Links

eLC

Tutoring resources (includes some paid tutor options)

  • The math department offers some free study halls many afternoons in Boyd, though I don't know how useful they are for 4000-level courses.
  • (I'm not sure how tutor availability differs for the summer as well.)

Class Schedule

All textbook sections come from the course textbook. Your homework sets also use many problems from that textbook.

  • The problem text may be recopied in homework assignments, so that you can do problems without having to keep your book open all the time.
  • For more details, consult the syllabus.

 

Don't forget about handouts that are attached in this calendar, such as group-work solutions and HW assignments.

  • Partial solution sets can instead be found on eLC.

 

Expect this calendar to be updated several times a week.


UNIT 1: Fundamentals of Z, gcds, and modular congruence

Week 1:

  • Tues Jun 5, 2018: Section 1.1. Introduction to basic + and * laws, recap of proof by induction.
  • Wed Jun 6: Section 1.1. Induction practice, the Binomial Theorem.
  • Thu Jun 7: Section 1.2. Divisors, Euclidean division (quotient and remainder), common divisors.
  • Fri Jun 8: Section 1.2. Euclidean Algorithm practice, linear combinations ax + by for integers x,y.

 

HW 1 - due Monday Jun 11

  • Every student must hand in all the required problems. Students in MATH 6000 must do at least one challenge problem.
  • Any challenge problems completed beyond this minimum are counted as extra credit.

 

If you're having a hard time getting the textbook, here's the first section's homework to tide you over for the moment.


Week 2:

 

HW 2 - due Friday Jun 15

 

TEST 1 will be Wednesday June 20.

  • Expect 5 to 7 questions, similar to HW level of difficulty, for a 60-minute test.
    • The first question always asks you to repeat definitions or to give very short examples.
  • This test covers material from Sections 1.1 to 1.4.
    • Section 2.1 won't show up on the test, but Section 1.4 will (despite not appearing on HW 1 or 2).
    • Make sure to go over your graded comments on HW sets!
  • Calculators will be allowed to help you do basic divisions, but you still have to show your steps for approaches like the Euclidean Algorithm.
  • Here's a topic list for the test.
  • Here are practice problems for the test.
    • We'll have an in-class review day, to go over your open questions or the practice problems, on Tuesday June 19.

Week 3:

  • Mon Jun 18: Section 2.1. Ordered rings.
  • Tues Jun 19: Test 1 Review
    • Review materials, such as practice problems, are located in the previous week's links.
  • Wed Jun 20: TEST 1
  • Thu Jun 21: Section 2.3. Basic computation in C, conjugates and magnitudes, polar form.
    • HW 3 is released now, due on Tues Jun 26.
  • Fri Jun 22: Section 2.3. Using polar form and DeMoivre's Theorem to determine roots of complex numbers.

 

HW 3 - due Tues Jun 26 (starts after Test 1)


UNIT 2: Complex numbers, polynomials, irreducibility tests

Week 4:

  • Mon Jun 25. Section 2.4. Quadratic and cubic equations in C.
  • Tue Jun 26. Section 3.1. Introduction to polynomials R[x], units in F[x], long division of polynomials.
  • Wed Jun 27. Section 3.1. The Root-Factor Theorem, GCD and the Euclidean Algorithm in F[x].
  • Thu Jun 28. Section 3.1. Irreducible elements of F[x], Fundamental Theorem for F[x], a result about partial fraction decompositions.
  • Fri Jun 29. Section 3.3 (day 1). Checking polynomials in Q[x] for rational roots, factoring via the Method of Undetermined Coefficients.
    • HW 4 is due today. Start HW 5 as well!
    • You may want to read ahead in Section 3.3 to help with HW 5! Eisenstein's Criterion is especially useful.

 

HW 4 - due Fri Jun 29

HW 5 (shorter) - due Tues Jul 3

  • You may want to read ahead in Section 3.3 in the book (especially Eisenstein's Criterion) over the weekend.

Week 5:

  • Mon Jul 2. Section 3.3. Using mods and primes to study irreducibility: Eisenstein's Criterion.
  • Tue Jul 3. Sections 3.1 and briefly introduce 3.2. Calculations with polynomial mods, set the stage for F[alpha].
    • HW 5 is due today. (See its download link above.)
    • Group-work
  • No class on Wed Jul 4 (national holiday).
  • Thu Jul 5. Test 2 Review. (See links below.)
  • Fri Jul 6. TEST 2

 

TEST 2 is on Friday, July 6.

  • Like Test 1, expect 5 to 7 questions in 60 minutes, with definitions and/or examples coming first.
    • This can include restating a theorem precisely. (See the practice test.)
  • This test covers Sections 2.3, 3.1, and 3.3.
    • While it is nice to know the quadratic formula, other than that, Section 2.4 is not covered.
  • Calculators are allowed again.
  • Here's a topic list for the test.
  • Here are some practice questions for this test.
    • We will go over review on Thursday July 5.

UNIT 3: Vector spaces, adjoining elements to create F[alpha], ring ideals and the Fundamental Homomorphism Theorem

Week 6:

  • Mon Jul 9. Section 5.1 (and brief recap of material from Tue Jul 3). Vector spaces over a field F, subspaces, span of a set of vectors.
  • Tues Jul 10. Section 5.1. Linear independence, basis, and dimension.
  • Wed Jul 11. Section 5.1 and Section 3.2. Linear maps, the definition of F[alpha], field degree [K : F] = dim(K) over F, "Degree Extension Formula" (Theorem 1.3).
  • Thu Jul 12. Section 3.2. Proving F[alpha] is a field, computations in F[alpha] using minimal polynomials.
    • HW 6 is due today.
  • Fri Jul 13. Section 3.2. More practice with F[alpha]. Comparing different extensions F[alpha] and F[beta].

 

HW 6 - due Thu Jul 12

HW 7 - due Tue Jul 17

  • This homework deals with pretty difficult ideas: I suggest office hours before the weekend to clarify key ideas!
  • The handout for Friday's class should be really useful here, though it's a lot to process. (The book doesn't present these ideas as systematically as I'd like.)

Week 7:

  • Mon Jul 16. Section 3.2, and start 4.1. More practice with F[alpha,beta], splitting fields. Definition of morphism.
  • Tue Jul 17. Section 4.1. Morphisms examples involving F[alpha], definition of ideal I <= R.
  • Wed Jul 18. Section 4.1. Principal ideals <a>, maximal ideals, congruence mod I.
  • Thu Jul 19. Sections 4.1 and 4.2. The quotient ring R/I, definition of isomorphism.
  • Fri Jul 20. Section 4.2. More isomorphism examples, Fundamental Homomorphism Theorem (FHT).

 

HW 8 - due Mon Jul 23

  • This is the last HW set of the course. You get a while to work on it, but it has a lot of abstract ideas!
  • Make sure to look over handouts above, including group-work solutions. They should help a lot.

 

TEST 3 is on Wednesday, July 25.


Week 8:

  • Mon Jul 23. Miscellaneous topics from Sections 5.3 and 4.2. Finite fields of size p^n, examples of product rings R x S.
    • This is not covered on Test 3, but some examples with R x S could be on the final.
    • (Also, the skills used in this day's notes should be good review / enrichment in preparation for Test 3.)
  • Tue Jul 24. Test 3 Review (see links above in Week 7).
  • Wed Jul 25TEST 3
  • Thu Jul 26. Section 5.2. Constructible numbers with straightedge and compass.
    • If this shows up on the final exam, it will only be one short question.
  • Fri Jul 27. Review day for the final exam!

 

Details about the final exam are below. 



Final exam details

Mon July 30, 2018

8:00am to 11:00am (try to show up a bit early to get yourself settled)

Boyd 323 (our usual classroom)

  • This exam will cover all the material from the three in-class exams.
    • Expect somewhere on the order of 11 to 13 questions, fairly similar to previous test questions. This should be around twice the length of an in-class test.
  • No bathroom breaks once the test starts. Talk to me if this is an issue.
  • You'll have to leave your backpack (or similar containers) at the side of the room during the test. Turn phones and smart watches off.


Last updated: 7/27/2018