Category Archives: Teaching

MAT 331 Spring 2015

Basic Info

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Instructor
Prof. Graham Leuschke
gjleusch@syr.edu
Time & Place
TR 9:30–10:50 in Carnegie 100
Textbook
Linear Algebra and its Applications, David C. Lay, Addison-Wesley, ISBN 0-321-38517-9.
Office Hours
MW 3-4; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

WeBWorK

WeBWorK is the online homework system we will use in MAT 331. It is hosted by SU, and is free to use.

To access WeBWorK, go to http://webwork.syr.edu/webwork2/MAT_331_Leuschke_Spring_2015 (you may want to bookmark this link).

Your Username is your NetID, for example jqpublic.

Your Password is initially set to be your 9-digit SUID, but you should change it after logging in.

The number of attempts on most problems is unlimited (the exception is True/False problems). Problems can be done in any order. You don’t have to do them all at once. You can get a PDF file of the entire assignment and print it out to work offline.

Homework due dates appear on the calendar: click Calendar on the left.

Two lowest WeBWork scores will be dropped.

MAT 532 Fall 2014

Basic Info

Instructor
Prof. Graham Leuschke
gjleusch@syr.edu
Time & Place
TR 2:00–3:20 in Carnegie 316
Textbook
Peter J. Olver and Chehrzad Shakiban, Applied Linear Algebra (website)
Office Hours
Mon 2-4, Tues 10:30-12, Wed 3-4, Thurs 1-2; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Announcements

  • My office hours for finals week are M 2-4, T 10:30-12, and W 2-4. You can pick up your graded HW 13 at those times.
  • The final exam will be on Wednesday December 10 at 5:15pm. It will be cumulative, with an emphasis on the material since the second exam (modifications of Gram-Schmidt, orthogonal matrices, QR factorization, orthogonal projections, the Fredholm Alternative, and singular value decompositions).
  • The second midterm exam was postponed one week from the date in the syllabus. It was given in class on Thursday 13 November and covered up through page 230 (the “unmodified” Gram-Schmidt process).
  • The first midterm exam was given in class on 2 October. It covered up through section 3.3 on examples of inner products3.2 on norms.

Problem Sets

  • Here are some problems on the material that hasn’t been covered by any homework sets.
    • (Fredholm Alternative) 5.6.20 (and compare page 109 and problem 2.5.3)
    • (SVD) 8.5.1 cde for practice finding eigenvalues
    • (SVD) 8.5.2 for finding the SVD given the eigenvalues: (a) 3+sqrt(5), 3-sqrt(5), (b) 1 and 1, (c) 5sqrt(2) and 0, (d) 3, 2, and 0, (e) sqrt(7), sqrt(2), and 0 (f) 3, 1, and 0.
  • HW #13, due Thursday 4 Dec:
    • 5.3.1 (a,b,c)
    • 5.3.27 (a,b,c,d)
    • 5.3.28 (i) and (ii)
    • 5.4.1 (a,b,c)
    • 5.4.2 (a)
  • HW #12, due Thursday 20 Nov:
    • 5.2.17 (b,c)
    • 5.2.18 (b,c)
  • HW #11, due Thursday 13 Nov:
    • 5.1.1 (a,b,c,d)
    • 5.1.5 (all)
    • 5.1.21 (b)
    • 5.1.25
    • 5.2.1 (b,c)
    • 5.2.8 part (i) (b,c)
  • HW #10, due Thursday 6 Nov:
    • 4.3.1
    • 4.3.7
    • 4.3.15 (b,c) and also compute the error
    • 4.4.1 (a,b)
    • 4.4.5
    • 4.4.12 (b,c)
  • HW #9, due Thursday 30 Oct:
    • 6.2.1(b,c,d)
    • 6.2.2
    • 6.2.4
    • 4.2.1
    • 4.2.3(a,c)
    • 4.2.5(a,c)
    • 6.1.13(b,c)
  • HW #8, due Thursday 23 Oct:
    • 6.1.1
    • 6.1.2
    • 6.1.3
    • 6.1.4(a)
    • 6.1.8(a)
  • HW #7, due Thursday 16 Oct:
    • 3.4.1 (b,d,f)
    • 3.4.22 (parts a and b for problems (i),(iii), and (v))
    • 3.4.25
    • 3.4.27
    • 3.5.2 (b,d,f)
    • 3.5.4
    • 3.5.19 (a,c)
  • HW #6, due Thursday 9 Oct:
    • 3.3.20 (a,c,d)
    • 3.3.28 (a,b,c)
    • 3.4.1 (b,d,f)
    • 3.4.22 (parts a and b for problems (i),(iii), and (v))
    • 3.4.25
    • 3.4.27
  • HW #5, due Thursday 2 Oct:
    • 3.1.19 (a,b)
    • 3.1.20 (a,b)
    • 3.2.1 (b,c)
    • 3.2.4 (a,b,c) (Equation (3.9) is at the bottom of p. 132)
    • 3.2.13 (a,b)
    • 3.3.2 (a,b,c)
    • 3.3.6 (a,b,c)
  • HW #4, due Thursday 25 Sept:
    • 2.3.21 (a,c,e)
    • 2.4.9 (a,b,c)
    • 2.5.2 (b,d,f)
    • 2.5.22
    • 2.5.24 (all parts, items (ii) and (v))
    • 2.6.1 (a,b,c,d)
    • 2.6.3 (a,b,c,d)
    • 2.6.4 (a,b,c,d)
  • HW #3, due Thursday 18 Sept:
    • 1.7.9 (b)
    • 11.4.14 (a,b) (on splines)
    • 1.7.16 (a,b,c)
    • 1.8.7 (b,d,g,i)
    • 1.8.23 (a,b)
    • 2.3.2
    • 2.3.9
  • HW #2, due Thursday 11 Sept:
    • 1.4.1 (a,c,e)
    • 1.4.3 (a; be sure to use GE exactly)
    • 1.4.15
    • 1.4.19 (a,b,d)
    • 1.4.20 (a)
    • 1.5.32 (a,c,e)
    • 1.6.25 (b,d)
  • HW #1, due Thursday 4 Sept:
    • 1.3.5
    • 1.3.14
    • 1.3.15
    • 1.3.22 (a,c,e,g)
    • 1.3.31 (a,c,e,g)

It has been said that ‘the human mind has never invented a labor-saving machine equal to algebra.’ If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines.

Josiah Willard Gibbs, 1887

MAT 534 Spring 2014

The course is over! Thanks to everyone for a great semester, and enjoy your summer.

Basic Info

Rubiks

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
Time & Place
MWF 9:30–10:25 in Carn 115
Textbook
Joseph A Gallian, Contemporary Abstract Algebra, 8th ed.
textbook website
Office Hours
MW 11-12, TR 2-3; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Announcements

  • The third midterm exam will be in class on Friday, April 25. It will cover Chapters 10 through 14 (up through ideals and factor rings).
  • The second midterm exam was in class on Friday, March 28. It covered up through Chapter 9 (normal subgroups and factor groups).
  • The first midterm exam was Friday, February 21, as in the syllabus. The exam covered up through Chapter 6 (Isomorphisms).

Links

  • Why all rings should have a 1, by Bjorn Poonen
  • Solutions to some of the homework: hw03, hw04, hw05
  • Keeler’s theorem and products of distinct transpositions: An episode of Futurama features a two-body mind-switching machine which will not work more than once on the same pair of bodies. After the Futurama community engages in a mind-switching spree, the question is asked, “Can the switching be undone so as to restore all minds to their original bodies?” Ken Keeler found an algorithm that undoes any mind-scrambling permutation with the aid of two “outsiders.” We refine Keeler’s result by providing a more efficient algorithm that uses the smallest possible number of switches.
  • Permutations and the 15-puzzle from class on 3 Feb. Skip to Section 5 for the good stuff, then come back to Section 4 for the details.
  • Group theory and Rubik’s Cube from class on 3 Feb. Skip to Section 3. There are about 519 quintillion conceivable configurations for the Rubik’s Cube, but only 1/12 of them are “valid”.

Problem Sets

MAT 733 Spring 2014

The course is over! Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your summer.

Basic Info

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Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
Time & Place
MW 12:45–2:05 in Carn 124
Textbook (optional)
H. Matsumura, Commutative Ring Theory
Office Hours
MW 11–12, TR 2–3; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Announcements/Links

  • Here’s a link to the translation of Emmy Noether’s paper, Idealtheorie in Ringbereichen
  • I suggest Googling around for an English translation of Serre’s “GAGA” paper.
  • Teacher: So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you’ll be pleasantly surprised.
    [The class laughs except for Bart who appears confused.]
    Teacher: Don’t you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

Problem Sets

MAT 631 Fall 2013

The course is over! Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your break.

Basic Info

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
AIM: leuschkeg
Google: leuschke@gmail
Time & Place
TR 9:30–10:50 in Carn 311
Textbook (optional)
Dummit & Foote, Abstract Algebra
Office Hours
MW 10:30–12:00; TR 3:00–4:00 (changed); by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus (Final Exam info is incorrect — see MySlice)

Announcement

Online evaluations are open through Dec 15. Please do them. Thanks.

Problem Sets

MAT 532 Fall 2013

The course is over! Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your break.

Basic Info

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
AIM: leuschkeg
Google: leuschke@gmail
Time & Place
TR 12:30–1:50 in Carn 311
Textbook
Peter J. Olver and Chehrzad Shakiban, Applied Linear Algebra (website)
Office Hours
MW 10:30–12:00; TR 3:00–4:00 (changed); by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus (Final Exam info is incorrect)

Announcements

  • Announcement
    Online evaluations are open through Dec 15. Please do them. Thanks.
  • The Final Exam is on Thursday 12 December, 5:15–7:15 pm in Carn 311 (the usual room). The syllabus has the wrong information.
  • The second midterm exam was Thursday, 31 October (boo!) in class. It covered Chapter 6 and Chapter 4 up through “Data Fitting” (fitting lines/parabolas/etc., not including “Least squares in function spaces”.
  • The first midterm exam was Thursday, 3 October, in class. It covered up through section 3.5 of the text.

Problem Sets

  • HW #1, due Tuesday 3 Sept: 1.3.5, 1.3.14, 1.3.15, 1.3.22 (a,c,e,g), 1.3.31 (a,c,e,g)
  • HW #2, due Tuesday 10 Sept: 1.3.2, 1.4.19 (a,b,d), 1.4.20 (a), 1.6.25 (b,d)
  • HW #3, due Tuesday 17 Sept: 1.7.16 (a,b,c), 1.8.7 (b,d), 1.8.23 (b), 2.3.2, 2.3.9, 2.3.21 (b,d)
  • HW #4, due Tuesday 24 Sept: 2.4.9 (a, b, c), 2.5.2 (b, d, f), 2.5.22, 2.6.1 (b ,d), 2.6.3 (b ,d ,e), 2.6.4 (b, d, e), 3.1.20
  • HW #5, due Tuesday 1 Oct: 3.2.1 (b, d, f does not exist — omit), 3.2.4 (a, b, c), 3.2.13 (a, b, c), 3.3.2 (a, b), 3.3.6 (a, b, c), 3.3.28 (b, d, f), 3.4.1 (b, d, f)
  • HW #6, due Tuesday 8 Oct: 3.4.22 (questions a and b for parts (i), (iii), (v)), 3.4.25, 3.4.27, 3.5.2 (b, d, f), 3.5.4, 3.5.19
  • HW #7, due Tuesday 15 Oct: 6.1.1, 6.1.2, 6.1.4(a), 6.1.8(a), 6.2.1(b, c, d)
  • HW #8, due Tuesday 22 Oct: 6.2.2, 6.2.4, 6.3.5 (a,b)
  • HW #9, due Tuesday 29 Oct: 6.3.7, 4.2.1, 4.2.3 (b, d), 4.2.5 (b, d), 6.1.13 (b), 6.1.16 (a, b). By the way, here is the scoop on Gauss and Ceres.
  • HW #10, due Tuesday 5 NovThursday 7 Nov: 4.3.1, 4.3.7, 4.4.1 (a, b, c), 4.4.5 From now on, homework will be due on Thursdays.
  • HW #11, due Thursday 14 Nov: 5.1.1 (b, d, f), 5.1.3 (b, d, f), 5.1.21 (b only), 5.2.1 (b), 5.2.2 (b), 5.2.8 (i and ii), 5.2.17 (b), 5.2.18 (b)
  • HW #12, due Thursday 21 Nov: 5.3.1 (b, d, f), 5.3.27 (b, d, f), 5.3.30 (only redo 5.3.27 (b))
  • HW #13, due Thursday 5 Dec: 5.4.1 (a, b), 5.5.4, 5.5.15 (b), 5.6.1 (b, c, d), 5.6.20 (a, b), 5.7.1 (a, b). You’ll have to come get your graded assignment from me between the last day of classes and the final.

It has been said that ‘the human mind has never invented a labor-saving machine equal to algebra.’ If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines.

Josiah Willard Gibbs, 1887

MAT 532 Fall 2012

The course is over! Final grades have been submitted to MySlice. Thanks to everyone for a great semester, and enjoy your break.

Basic Info

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
AIM: leuschkeg
Google: leuschke@gmail
Time & Place
TR 9:30–10:50 in Carn 300
Textbook
Carl D. Meyer, Matrix Analysis and Applied Linear Algebra
Office Hours
MW 1:30–4:30; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Announcements

Here is last year’s final exam. As always, it should be used with caution: we did not cover exactly the same material this year. Also, this year’s final will have a large section consisting of definitions and formulas, like Exam II.

Exam II was in class on Thursday 29 November. It covered up through orthogonal projections and reflections, that is, Sections 5.1–5.6, plus the PageRank material. Here is last fall’s Exam II for your reference. Note that we did not cover exactly the same material this year. Also I announced in class that about half the points on this exam will be “theoretical” questions: definitions and formulas, rather than computations.

Exam I was in class on Tuesday 9 October. It covered up through least-squares, that is, all of the material we covered from Chapters 1–4. Here is last fall’s Exam I for your reference. Note that we did not cover exactly the same material before the first exam this semester as last year.

It has been said that ‘the human mind has never invented a labor-saving machine equal to algebra.’ If this be true, it is but natural and proper that an age like our own, characterized by the multiplication of labor-saving machinery, should be distinguished by the unexampled development of this most refined and most beautiful of machines.

Josiah Willard Gibbs, 1887

Problem Sets

Links

MAT 631 Fall 2012

The course is over! Final grades will soon be submitted to MySlice. Thanks to everyone for a great semester, and enjoy your break.

Basic Info

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
AIM: leuschkeg
Google: leuschke@gmail
Time & Place
TR 12:30–1:50 in Carn 311
Textbook (optional)
Dummit & Foote, Abstract Algebra
Office Hours
MW 1:30–4:30; by appointment; and any time my door is open (317G Carnegie)
Important documents
syllabus

Problem Sets

Links

MAT 296 Spring 2012

(Mostly a placeholder at the time, and now a historical artifact.)

Basic Info

Instructor
Prof. Graham Leuschke
email: gjleusch@math.syr.edu
AIM: leuschkeg
Google: leuschke@gmail
Time & Place
MWF 9:30–10:25 in Gifford auditorium
Textbook
Stewart, Calculus: Early Transcendentals, 7th edition
Office Hours
TBA; by appointment; and any time my door is open (206C Carnegie)
Important documents
syllabus for all sections
supplement to the syllabus for my section

Announcements

Handouts, Slides, Review Sheets, and Study Guides