Teaching at UC Davis, Summer 2020

MAT-108, Introduction to Abstract Mathematics: MTWF 1000-1140 AM     Join via Zoom on Canvas.

PREREQUISITES: A good working knowledge of calculus (courses MAT 21AB) and some linear algebra (MAT 22A, may be taken concurrently). You are responsible for satisfying the prerequisites!

OFFICE HOURS: (I do not reply any emails on weekends) W 09:00-09:55 AM   Join via Zoom on Canvas, or use any of the following options:

Join Zoom Meeting
https://ucdavis.zoom.us/j/94251745439

Meeting ID: 942 5174 5439

TEXTBOOK: A Transition to Advanced Mathematics, 8th Edition by D. Smith, M. Eggen and R. St. Andre. Brooks-Cole, 2015.

COVERED SECTIONS:  1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 4.1, 4.2, 4.3, 4.4, 4.5, 5.1, 5.2, 5.3, 5.4, 6.1, 6.2, 6.3, 6.4

LECTURE NOTES: If you want to write your own lecture notes, use the current blank slides HERE. Otherwise, download the final versions below:

  1. Week 1:   06/22                    06/24                  06/26
  2. Week 2:  06/29    06/30        07/01                  Holiday(NO class)        SEE the Sample Review Homework HERE
  3. Week 3:  07/06    07/07        07/08                 Rev_HW
  4. Week 4:  07/13    07/14        07/15                   07/17
  5. Week 5:  07/20    07/21        07/22                  07/24
  6. Week 6:  07/27      OH           07/29                  Final
  7. Some Problems from Office Hours. From_07/07.     Some HINTS to HW4   Some Hints_to_HW5

OPTIONAL READING: (For examples and exercises)

GRADE: We will use Canvas for grading. Course grade will be based on the following:

  • 5 Homeworks: 20 points each
  • Review Homework  (Friday, July 10. From 10AM to 5PM):                                                                                    100 points
  • Self-Video for Review Homework (2-4 minutes, Due 07/10 at 5PM), a video explaining your solutions:      10 points
  • Final (Friday, Friday, July 31. From 10AM to 10PM).  It covers the whole course:                                             200 points
  • Self-Video for Final (3-5 minutes, Due 07/31 at 10PM):                                                                                              20 points
  • TOTAL: 430 points.

IMPORTANT DATES:

  • 06/22 (Mon) Homework 1
  • 06/25 (Thu)  Due HW1
  • 06/29 (Mon)  Homework 2
  • 07/02 (Thu)  Due HW2
  • 07/03 (Fri)  Sample Review Homework (AVAILABLE HERE for download) and  NO class
  • 07/07 (Tue) Sample Self-Video                  AVAILABLE for download on Canvas -> Files -> SelfVideo.mp4
  • 07/10 (Fri)  Review Homework and Self-Video  (Due at 5:00PM, so make sure to have a strong internet connection and a recording device this day)
  • 07/13 (Mon)  Homework 3
  • 07/16 (Thu)  Due HW3
  • 07/17 (Fri)    Homework 4
  • 07/21 (Tue)  Due HW4
  • 07/23 (Thu) Sample Final                AVAILABLE HERE for download!    Solutions to Problem_5 
  • 07/24 (Fri)   Homework 5
  • 07/28 (Tue)  Due HW5
  • 07/31 (Fri)  Final Exam and Self-Video       (Due at 10:00PM, so make sure to have a strong internet connection and a recording device this day)

 

HOMEWORKS:    All of them are Due at 5:00PM. Solve and upload your solutions to ALL problems on Canvas (pdf and jpg files are fine); after the Due, only 4 problems will be randomly selected and graded, each is worth 5 points.

  • Homework_1.   1.1: 3(g), 6(d), 9(f), 10(e)               1.2: 6(i), 7(e), 12(d), 16(i)               1.3: 6(d), 8(j), 10(b)                 1.4: 5(d), 7(l), 9(c), 11(a)   CORRECTED SOLUTIONS!!!

 From now on, we will use the numeration from the 7th Edition scan below.        SEE SOLUTIONS FOR HW1 and HW2.

  • Homework_2.   1.5: 3f, 5b, 7d                1.6: 4d, 6l, 7i              2.1: 5l, 15d, 17f            2.2: 9g, 11f, 19c            2.3: 1k           2.4: 6h, 7c                    SOLUTIONS!!! 
  • Review_HW.    INSTRUCTIONS: The Review Homework will be posted HERE this Friday 07/10 at 10AM. It is worth 100 points, will be based on ALL covered sections from 1.1 to 3.2 (see for instance, the sample Review HW above), and you are allowed to use the book or lecture notes, if needed. You have to solve it before midday (so, 2 hours duration). Printing the Homework is optional, you can use a device (like Ipad) or any piece of paper, just make sure to write your Name, Signature and ID wherever you write your solutions. Then you have time from 12:01PM to 5:00PM to prepare your self-video and submit everything on Canvas. On 07/10, I will be available on Zoom from 10AM to 10:30AM, just in case you are having technical problems (otherwise, you do NOT need to show up on Zoom, since there will be NO class on that day), however, I will NOT answer any questions related to interpretations of the homework.
  • ABOUT THE SELF-VIDEO: You have to show your face at least when you are introducing yourself. It is ok to literally read SOME parts of your written solutions, however, just reading your solutions without any explanations (by using different words) WILL COUNT as 0/10 POINTS.
  • REVIEW HOMEWORK: Download HERE.   See SOLUTIONS
  • Homework_3:    3.3: 2f, 3e, 5, 6e           4.1: 6c, 8b, 11d, 19a          4.2: 11, 12, 14e           4.3: 1i, 3c, 8f, 14e  
  • Homework_4:    4.4: 1e, 2e, 8, 9b          4.5: 2f, 4f, 10f, 14          5.1: 11b, 16b, 18a, 21a        5.2: 3h, 5f        (Change: Think about 5.2.7f, but do NOT deliver it)   
  •  
  • Instructions, Feedback and Tips for Final Video: Download HERE!  
  • Homework_5:    5.3: 9b, 10e, 12c         5.4: 5c, 8c, 12, 16c         6.1: 5, 11c, 16a           6.2: 14a, 17, 20d, 23a            Scan for Section 5.4             (Do NOT deliver: 6.3: 2d, 5, 13)                         Scan_for_Ch6
  • SOLUTIONS to Homeworks:   HW3       HW4         HW5  (there could be typos)

 

FINAL EXAM         Download_HERE!!!         SOLUTIONS (check them before you write me any email)

(To be published here AT 10:00AM, due 07/31 at 10:00PM) ALL covered sections will be evaluated!!!

 

Grading curve: Will be set at the end of the course, depending on the mean (over all students) of the total number of points. However, students having less than 40% will be assigned grade F and students in the range 41-50% will be assigned grade D.

PRACTICE EXERCISES FROM 7th Edition and Continuation WITH SOLUTIONS: (Solve all problems by yourself first, then compare the solutions)

  • 1.1: 3(h), 4(d), 6(h), 9(a), 10(b);      1.2: 3(e), 5(d), 6(b), 7(a), 12(f), 16(b);        1.3: 6(c), 8(c), 10(c), 10(e);      1.4: 4(b), 5(f), 6(f), 8(a), 9(d), 11(b).

    Solutions.

  • 1.5: 3(g), 4(c), 5(c), 6(e), 7(b), 12(d);         1.6: 4(b), 4(c), 4(g), 5(a), 6(i), 7(h).         Solutions.

  • 2.1: 5(d), 5(j), 6(d), 14(d), 15(c), 15(h), 17(d), 19(g);                     2.2: 1(j), 2(f), 9(b), 9(c), 11(b), 12(b), 12(c), 19(f).

    2.3: 1(n);                  2.4: 6(g), 7(a), 7(h), 8(h), 13(c).              Solutions.

  • 2.5: 1(b), 2, 5(b), 5(c), 13(c);                 3.1: 2(b), 4(d), 5(a), 5(h), 7(c), 7(d), 7(f), 15(c).          Solutions.

  • 3.2: 1(b), 1(c), 1(f), 5(b), 5(e), 5(f), 5(h), 7(b), 7(d), 9(a), 11, 12, 13(c), 19(d);                     3.3: 2(a), 2(c), 3(a), 3(d), 4, 7(b), 7(c), 15(c).

    4.1: 1(b), 1(c), 1(i) (In problem 1, one codomain suffices), 4(d), 6(d), 11(e), 19(e).             Solutions.

  • 4.2: 10, 13, 14(c), 14(d);          4.3: 1(b), 1(d), 1(f), 1(h), 1(l), 2(b), 2(d), 2(f), 2(h), 2(l), 3(c), 6, 8(c), 8(d), 14(c).       Solutions.

  • 4.4: 1(a), 2(b), 2(c) (find a simpler function than 3(d)!), 3(a), 3(d), 5(b);

    4.5: 2(b), 2(e), 5(a), 5(b), 10(a), 10(b), 13, 18(a), 18(b). Also, find a counterexample to equality in 10(a).          Solutions.

  • 5.1: 2(k), 2(l), 2(m), 2(o), 4, 6(b), 11(d), 12, 21(b), 22(a);                                 5.2: 3(c), 4(c), 7(b), 7(d), 7(g), 12(b).

    5.3: 2, 9(c), 9(e), 9(f), 10(a), 10(b), 10(d), 13(a), 14(a), 14(b);                         5.4: 2, 5(a), 5(e), 8(b).                      Solutions.

 

ADDITIONAL POLICIES:

Use of books, notes, calculators, or anything else but pencil and paper, will not be allowed in the final (you will sign the Honor Statement).

Talking, texting, newspaper reading, etc. disrupt the lectures, use electronic devices for non-academic purposes during lectures is prohibited.

If you have any problem at all that requires special accomodation, please let me know well in advance!

There will be no make-up homeworks nor make-up exams. A missed exam counts as 0 points. If you miss the final you will automatically receive an F. The grade I (Incomplete) will not be given in any circumstances.

 

Teaching at UC Davis, Winter 2020

TEACHER OFFICE HOURS: M 03:05-04:05PM  and  R 01:30-03:00PM

MAT-145 s001, Combinatorics: MWF 1210-0100 PM                                              MAT-145 s002, Combinatorics: MWF 0210-0300 PM

TA: Brett Leroux (leroux AT math.ucdavis.edu)    Office Hours: T 12-1PM,   T 3-4PM   and  W 10AM-12.  Room: 2142 Academic Surge.

TEXTBOOK: Combinatorics and Graph Theory, 2nd Edition by Harris, Hirst and Mossinghoff. Springer. 2008.

  • Sample Midterm1.            Solutions.   
  • Hints to some Problems:     2.2.8.     2.5.13
  • Midterm 1 will be based on the Suggested Exercises and Homeworks 1 and 2. It means Sections:   2.1, 2.2, 2.3, 2.4, 2.5 and 2.6.4
  • Remember to bring your photo ID, pen/pencil and eraser ONLY.
  • Sample Midterm 2.           Solutions.
  • Midterm 2 will be based on the Sugg. Exercises and HW 3 and 4. Sections:  2.6.5, 2.6.2, 1.1.2, 1.1.3, 1.3.1, 1.3.2, 1.4.2 and 1.5.1.
  • TakeHome Exam will cover ALL sections!
  • IMPORTANT FINAL MODIFICATIONS (Due to current global health issues):
  1. There will be NO Final Exam.
  2. All students have been assigned a grade in Canvas, proportional to current sum/250 points. If you want this to be your final grade, then you are set, have a nice break!
  3. If you want to improve your grade, you will have the option to submit a TakeHome Exam, worth 100 points (so final grade will be proportional to sum/350 points), to be released in this site on 03/17 at 6pm, and due on 03/18 at 3pm, online submission via canvas.
  4. Let me know about your choice (via email) by 03/18 at 3pm.
  5. If you have any questions, let us communicate via email.
  6. Clarification about the TakeHome Exam: If you obtain at most 70 points in the exam, then after averaging, your final grade could be lower than your current grade. But, if you obtain more than 70 points, then your final grade will never be lower than your current grade.
  7. TAKEHOME EXAM: Use this LINK to download it. Ready!!!  Read, sign and submit the first page with your solutions.

 

SUGGESTED EXERCISES (By section)

  • 2.1:  1, 2, 3, 4, 8, 9, 11, 12, 14.
  • 2.2:  2, 3, 5, 6, 7, 8, 10, 11.
  • Extra: Use induction to prove:   \((a) \ 11^n-6\) is divisible by 5, \(\forall n\in\mathbb N\).        \((b) \ n^2<2^n,\ \forall n\ge 5\).
  • 2.3:  1, 2, 3, 4, 5, 6, 8, 9, 10.
  • 2.4:  1, 2, 3, 5, 6, 7, 8, 9, 10, 13.
  • 2.5:  1, 2, 3, 4, 6, 7, 8, 9, 12.
  • 2.6.4:  All of them.
  • 2.6.5:  All except Problem 5.
  • 2.6.2:  1, 3, 4, 5, 6, 9.
  • 1.1.1:  1, 3.
  • 1.1.2:  1, 3, 4, 5, 6, 8, 12, 14, 16.
  • 1.1.3:  1, 2, 3, 6, 7.
  • 1.3.1:  1, 2, 3, 4.
  • 1.3.2:  1, 2, 3, 4, 7, 8, 10, 12.
  • 1.4.1:  1, 2, 3, 4.
  • 1.4.2:  1, 2, 4, 5, 6, 8.
  • 1.5.1:  1, 2, 3, 4, 5, 6.
  • 1.5.2:  All of them.
  • 1.7.1:  1, 2, 3.
  • 1.7.2:  1, 2, 3, 4, 5, 6.
  • 1.8.1:  1, 3, 4, 5.
  • 1.8.2:   1, 2, 4, 5.
  • 2.10.2:  2, 3, 4, 5, 6, 7, 8.

HOMEWORKS: All problems are worth the same, but elegant solutions to Difficulty 3 Problems could provide bonus points for Midterms.

  1. Homework_1.  Due on 01/22.
  2. Homework_2.  Due on 01/29.
  3. Homework_3.  Due on 02/14.
  4. Homework_4.  Due on 02/24.
  5. Homework_5.  Due on 03/13.

OPTIONAL READING: (For examples and exercises)

  • Discrete Mathematics: Elementary and Beyond by Lovász, Pelikán, and Vesztergombi. Springer. 2003.

GRADECourse grade will be based on the following:

  • 5 Homeworks: 10 points each         (due dates: Hw1: 1/22  //  Hw2: 1/29  //  Hw3, Hw4, Hw5: TBA)
  • Midterm Exam 1 (Friday, JAN 31, in class): 100 points,
  • Midterm Exam 2 (Friday, FEB 28, in class): 100 points,
  • Final (s001: Wednesday, March 18 // 1:00-3:00 p.m.//Room: TBA,----- s002: Tuesday, March 17 // 6:00-8:00 p.m.//Room: TBA): 200 points,
  • TOTAL: 450 points.

ADDITIONAL POLICIES:

All students must present their photo ID during exams. Use of books, notes, calculators, or anything else but pencil and paper, will not be allowed on any exam.

Talking, texting, newspaper reading, etc. disrupt the lectures, use of computers, cellphones, or any other electronic devices for non-academic purposes during lectures is prohibited.

If you have any problem at all that requires special accomodation, please let me know well in advance!

There will be no make-up quizzes nor make-up exams. A missed exam counts as 0 points. If you miss the final you will automatically receive an F. The grade I (Incomplete) will not be given in any circumstances.

 

Teaching at UC Davis, Fall 2019

TEACHER OFFICE HOURS: T 1100-1200 AM , T 0230-0330 PM and R 0100-0200 PM

MAT-135 AA, Probability: MWF 1100-1150 AM  ------ TA: Joshua Parker (jdparker AT math.ucdavis.edu)    Office Hours: W 0400-0600 PM

MAT-135 AB, Probability: MWF 0210-0300 PM  ------ TA: Zhongruo Wang (wangleft AT math.ucdavis.edu) Office Hours: M 0300-0500 PM

TEXTBOOKProbability and Random Processes, 3rd Edition by Geoffrey R. Grimmett and David R. Stirzaker; Oxford University Press.

Covered sections        1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.3, 3.1, 3.2, 3.3, 3.5, 3.6, 3.7, 3.8, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 5.7, 5.8, 5.9, 5.10

Homeworks will not be graded:

OPTIONAL READING: (As sources of examples and exercises)

  • A First Course in Probability, 10th Ed. by Sheldon Ross.
  • Lecture notes of Professor Gravner. [pdf]

GRADECourse grade will be based on the following:

  • 5 Quizzes during discussion sessions, lead by the TA: 10 points each quiz         (quiz days: Oct. 8,10, Oct. 15,17, Oct. 29,24, Nov. 5,7, Nov. 19,21)
  • Midterm Exam 1 (Wednesday, October 30, in class): 100 points,
  • Midterm Exam 2 (Monday, November 25, in class): 100 points,
  • Final (Friday, December 13//6:00-8:00 p.m, Monday, December 9//3:30-5:30 p.m): 200 points,
  • TOTAL: 450 points.

ADDITIONAL POLICIES:

All students must present their photo ID during exams. Use of books, notes, calculators, or anything else but pencil and paper, will not be allowed on any exam.

Talking, texting, newspaper reading, etc. disrupt the lectures. Use of computers, cellphones, or any other electronic devices for non-academic purposes during lectures is prohibited.

If you have any problem at all that requires special accomodation, please let me know well in advance!

There will be no make-up quizzes nor make-up exams (unless you have a valid justification with evidence, such as medical). A missed exam counts as 0 points. If you miss the final you will automatically receive an F. The grade I (Incomplete) will not be given in any circumstances.


Teaching at IMPA

Linear algebra and optimization (finance). Mar-May 2019

TA: Dyego Soares de Araújo  (dyego.eu AT gmail.com)

References

  • LIMA, E. L. – Álgebra Linear. Coleção Matemática Universitária, IMPA, 1995.
  • STRANG, G. – Introduction to Linear Algebra. Wellesley-Cambridge Press, 1993.

Graduate Teaching Assistant at IMPA

  1. Real analysis. Jan-Fev 2017, Jan-Fev 2018, Jan-Fev 2019
  2. Mathematical methods in finance. Mar-Nov 2018
  3. PDEs in finance. Sep-Nov 2017
  4. Probability. Jun-Aug 2017
  5. Linear PDE theory. Oct-Nov 2016
  6. Markov chains. Jan-Fev 2016
  7. Analysis in \(\mathbb R^n\). Mar-Jun 2015, Mar-Jun 2016

 

Teaching at the Universidad de Cordoba - Colombia

  1. ODEs. 2012
  2. Calculus. 2012