## Tsinghua-BIMSA Learning Seminar on Multiple Zeta Values, Yau Mathematical Sciences Center (YMSC), Tsinghua University, 2021-2022

Starting November 26th, together with faculty and PhD students at BIMSA-Tsinghua such as Chenglong Yu, Zhiwei Zheng, Li Lai we will organize a learning seminar on multiple zeta values. This seminar is inteded for people who want to learn more about the subject and it will follow the book of Jose Burgos Gill and Javier Fresan, Multiple Zeta Values: from numbers to motives.

The schedule will be updated periodically on this webpage and on YMSC seminar page as well.

**Organizer：**Chenglong Yu, Zhiwei Zheng, Li Lai, Cezar Lupu**Time： **Friday 1:30-3:30pm，2021-2022**Venue：**Lecture hall, 3rd floor of Jin Chun Yuan West Building, YMSC, Tsinghua University

**Seminar 1.** *An introduction to the Riemann zeta and multiple zeta functions and their special values.* **Speaker: **Cezar Lupu**Abstract: **In this first talk, we introduce the multiple zeta functions and their values. We explore the basic properties such as convergence, analytic continuation, their relations and some special values. This talk is also suitable for graduate students and advanced undergraduate students.

**Seminar 2.** *Multiple zeta values. Basic properties and identities.***Speaker: **Cezar Lupu**Abstract: **In this second talk, we explore more the linear relations among multiple zeta values and we study a little bit more the -vector space of multiple zeta values of a given weight. Also, using generating functions and properties of special functions, we prove some well-known identities for MZV’s in the literature.

## The 2021 Math Olympiad Summer Program (MOP), June 7-25, online

The 2021 Mathematical Olympiad Summer Program will take place online via Zoom between June 7-25. The camp is organized by the Mathematical Association of America and it is run by the CMU faculty Po-Shen Loh (director) with the help of other instructors (faculty, postdocs and Ph.D. students) from schools such as Massachusetts Institute of Technology (MIT), Stanford University, Harvard University, North Carolina State University, Carnegie Mellon University (CMU), Princeton University, Ohio State University, Colorado State University, Cornell University, University of Washington Seattle and Texas Tech University.

- Students will be separated into four groups.
- Black (~13 students): approx IMO gold;
- Blue (~13 students): approx IMO silver;
- Green (~13 students): approx IMO bronze;
- Red 1 (~13 students): approx IMO honorable mention;
- Red 2 (~13 students): approx IMO honorable mention;

- The timetable will be (all times Eastern):
- Noon – 1:30pm (Class)
- 2:00pm – 4:00pm (90-min-Class/Test/Quiz/Other). Note that if a Class is in this slot, it is only 90 minutes.
- 4:00pm – 6:30pm (Test/Quiz-Review/Other)
- 7:00pm – 8:00pm (Test Review or Optional non-Olympiad seminar)
- 8:30pm – 9:00pm (Panel)

My schedule consists of 10 lectures and one seminar. More details are given below:

**Lecture 1**.* Irreducible polynomials.*

Group: Red 2, June 7

Location: online via Zoom

**Lecture 2**. *Irreducible polynomials*.

Group: Red 1, June 7

Location: online via Zoom

**Lecture 3**.* Irreducible polynomials*.

Group: Green, June 9

Location: online via Zoom

**Lecture 4**.* **Irreducible polynomials*.

Group: Blue, June 10

Location: online via Zoom

**Lecture 5**.* **Romanian Olympiad (Algebra) gems*.

Group: Black, June 14

Location: online via Zoom

**Seminar**. *Mean value theorems and applications*.

Group: Black, Blue, Red 1 & 2 & Green, June 12

Location: online via Zoom

**Lecture 6**. *Algebraic integers and applications*.

Group: Green, June 22

Location: online via Zoom

**Lecture 7**.* Sequences and series of real numbers: inequalities and asymptotics*.

Group: Blue, June 23

Location: online via Zoom

**Lecture 8**. *Sequences and series of real numbers: inequalities and asymptotics*.

Group: Black, June 24

Location: online via Zoom

**Lecture 9**. *Algebraic integers and applications*.

Group: Red 1, June 25

Location: online via Zoom

**Lecture 10**. *Algebraic integers and applications*.

Group: Red 2, June 25

## Lectures on MATH 1451-Calculus I with Applications, Texas Tech University-Spring 2021

This playlist collects the lectures (synchronous) on Calculus I with Applications that I taught at Texas Tech University during the Spring Term of 2021. The lectures were recorded via Zoom for online-distance teaching during the COVID-19 pandemic. They are publicly available under information on the course, and course material (with embedded, time-stamped links to the YouTube videos) can be found at https://lupucezar.wordpress.com/teaching/.

Lecture 1 (Graph and functions)

Lecture 2 (Inverse functions)

Lecture 3 (Limits)

Lecture 4 (Algebraic computation of limits)

Lecture 5 (Continuity)

Lecture 6 (Exponentials and logarithms)

Lecture 7 (Derivatives-part 1)

Lecture 8 (Derivatives-part 2)

Lecture 9 (Rules of derivatives)

Lecture 10 (Derivatives of trigonometric, exponential and logarithmic functions)

Lecture 11 (Applications of derivatives in physics)

Lecture 12 (Chain rule)

Lecture 13 (Implicit differentiation)

Lecture 14 (Exponential, logarithmic differentiation and related rates)

Lecture 15 (Linear approximation and differentials-part 1)

Lecture 16 (Linear approximation and differentials-part 2)

Review session for midterm exam

Lecture 17 (Extreme values of continuous functions)

Lecture 18 (Mean value theorems)

Lecture 19 (Sketching the graph of a function)

Lecture 20 (Curve sketching with asymptotes: Limits involving infinity)

Lecture 21 (L’Hospital)

Lecture 22 (Optimization in physical sciences, engineering, business, biology)

Lecture 23 (Antidifferentiation)

Lecture 24 (Area as the limit of a sum)

Lecture 25 (The definite integral)

Lecture 26 (The fundamental theorem of calculus)

Lecture 27 (integration by substitution)

Lecture 28 (The Mean value theorem for integrals: the average value)

Lecture 29 (Numerical integration formulas)

## MATH 1451-Calculus I with Applications, Spring 2021, Texas Tech University

Course description and purpose

This course introduces students to calculus, in particular, to solving problems in differentiation and integration and applying these concepts to problem solving and real world applications. This is not intended to be a course in abstract mathematics. However, some mathematical rigor, with proofs, is expected.

Students learn how to perform . Mainly, we shall cover the following topics:

**Functions and Graphs.**1.1 What is Calculus?

1.2 Preliminaries.

1.3 Lines in the plane; parametric equations.

1.4 Functions and graphs.

1.5. Inverse functions; inverse trigonometric functions.**Limits and Continuity**2.1 The limit of a function.

2.2 Algebraic computation of limits.

2.3 Continuity.

2.4 Exponential and logarithmic functions.**Differentiation.**3.1 An introduction to the derivative: tangents.

3.2 Techniques of differentiation.

3.3 Derivatives of trigonometric, exponential, and logarithmic functions.

3.4 Rates of change: modeling rectilinear motion.

3.5 The chain rule.

3.6 Implicit differentiation.

3.7 Related rates and applications.

3.8 Linear approximation and differentials.**Additional applications and derivatives and integrals.**5.1 Extreme values of a continuous function.

5.2 The mean values theorem.

5.3 Using derivatives to sketch the graph of a function.

5.4 Curve sketching with asymptotics: limits involving infinity.

5.5 L’Hospital rule.

5.6 Optimization in the physical sciences and engineering.**Integration.**4.1 Antidifferentiation.

4.2 Area as the limit of a sum.

4.3 Riemann sums and definite integrals.

4.4 The fundamental theorem of calculus.

4.5 Integration by substitution.

4.6 The mean value theorem for integrals; average value.

4.7 Numerical integration: the trapeizodal rule and Simpson’s rule.

Course number, office hours and webpage

- MATH 1351-CALCULUS I WITH APPLICATIONS, Main Campus (TTU Mechanical Engineering South Building)
- Lecturer: Cezar Lupu (Postdoctoral scholar)
- Topics covered: functions and graphs, limits of functions, continuity, differentiability and integration.
- Office hours: Monday & Wednesday (2-3 PM), and by appointment via e-mail
- Webpage: https://lupucezar.wordpress.com/teaching/

Schedule and locations for live discussions\office hours

**Monday & Wednesday, 12:30-1:50 PM**via Zoom (the Zoom link will be sent via email) for lectures and discussions over the materials (lecture notes, slides, and videos) sent in advance. The office hours are on**Monday & Wednesday, 2-3 PM**.- Tentative schedule

Policies, grading criteria, homework, exams and references

The grade will be determined by the following three factors:

*2 Gateway exams: 20% (each worth 10%)**Homework assignments (WebWork) 25%**Midterm Exam: 30%**Final exam: 25%**Lectures attendance: 10% (EXTRA credit!)**Review sessions: 3% for each one of them (EXTRA credit!*)

The final examination is mandatory in order to pass the class.

Each gateway exam contains a set of 10 short questions on differentiation, respectively integration (derivatives and integrals to compute). Each gateway exam will take 30 minutes and will be scheduled by the instructor. Each gateway is administered at a unique time to the entire class – dates TBA. Procedural details will be provided in class. Midterm exams will be announced in advance in class and on my website. The final exam will be a 24 hours exam and it will take place on* Monday, May 10th online via Blackboard*. The final exam is comprehensive, i.e., it will examine material from the entire course. Final exam dates are set by the university-please confirm the date of our exam on the university website.

**Grade Inquiry Policy**: Any student who has questions about any grade received on an assessment should meet with the instructor in person, if possible, within a one-week period of receiving the graded assessment. At this meeting, the instructor will provide an explanation of the grading and computation of the score. Inquires received after the one-week period will not be considered.

**Calculator**: A graphing calculator is a useful tool for this course. However, calculators or other electronic devices will NOT be permitted on quizzes, online exams, and the final exam.

**Reading**: Reading the material from the textbook (paper or electronic form) is mandatory.

**WeBWorK:** WeBWorK is an internet-based method for delivering homework problems to

students. Visit the course webpage for more information on how to access WeBWorK and how to enter your solutions; see Helpful Documents. You will need your eRaider username and student ID number with the R to log into WeBWorK. The WeBWorK system responds by telling you whether an answer (or set of answers) is correct or incorrect and also records whether you answered the question correctly or incorrectly. You are free to try a problem as many times as you wish until the due date. It is your responsibility to check WeBWorK for new assignments.

Please do not wait until the day the assignment is due to begin and/or send questions. I will not answer questions e-mailed to me within 24 hours from the HW deadline.

**Regarding the Comprehensive Final Exam**: The common final represents a course requirement.

A student who did not complete the final exam, but otherwise completed all the other requirements successfully, cannot be assigned a passing letter grade. Each designated instructor has to keep his/her copy of partial scores and grades for each student for 2 calendar years from the date of recording the grade. The final exam will be given in a proctored environment. The date for the final exam was scheduled prior to start of the semester; the location will be announced at the end of the semester. The date and time of the exam cannot be changed. Final exam conflicts may arise only between two or more math courses, in which case the course with lowest number has priority in maintaining the exam date and time.

For the final exam, students should not purchase a blue book. The exam will be distributed with on paper, with spaces to fill in/fill out. No other printed materials and electronic devices are allowed during the final. Scratch papers may be checked by the instructors.

**Make-Up Policy**: There are no make-up exams except for absence due to religious observance or absence due to officially approved trips (see Class Attendance below). The student should make arrangements to take an exam and/or quiz prior to his/her absence. In the event that an advance notice cannot be provided, the student must contact the professor within a reasonable amount of time to discuss the missed assessment.

There are no make-up WeBWorK homework sets assignments except for absence due to religious observance or absence to due officially approved trips (see Class Attendance below). If a student misses a WeBWorK homework sets for one of the above reasons, the homework set will be reopened.

**Class Attendance**: Students are cautioned that active participation is necessary for success.

Attendance will be taken regularly. Students who miss no more than 2 weeks of classroom time during the whole semester will receive a bonus (extra credit) of 10% to their overall grade.

**During Exams, no electronic devices are allowed, including but not limited to: iPhones, smart watches, calculators of any kind, pagers. Please have all phones turned off and placed away during the classroom.**

**Letter grades** will then be assigned in accordance with the following correspondence:*Letter grade A = a percentile grade of 90% of higher**Letter grade B = a percentile grade of 80% or higher, that is lower than 90%**Letter grade C = a percentile grade of 70% or higher, that is lower than 80%**Letter grade D = a percentile grade of 60% or higher, that is lower than 70%**Letter grade F = a percentile grade lower than 60%*

The main reference include the following:

Accommodations and schedule conflicts

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both me and Student Disability Services in West Hall or call 806-742-2405, *before the end of the second week of classes*. Please see Operating Policy and Procedure 34.22 for a complete description of Texas Tech’s policy on accommodations or students with disabilities. Similarly, students who have any conflicts (including religious holy days) with the scheduled examination dates should notify me *before the end of the second week of classes*. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence.

Civility giudelines and syllabus addendum

Please see the attached documents regarding:

They were shared with all chairs by the Provost’s Office in view of the upcoming semesters.

## Lectures on MATH 1451-Calculus I with Applications, Texas Tech University-Fall 2020

This playlist collects the lectures (asynchronous) on Calculus I with Applications that I taught at Texas Tech University during the Fall Term of 2020. The lectures were recorded via Zoom for online-distance teaching during the COVID-19 pandemic. They are publicly available under information on the course, and course material (with embedded, time-stamped links to the YouTube videos) can be found at https://lupucezar.wordpress.com/teaching/.

**Zoom Lecture 1**. The big picture of calculus **Zoom Lecture 2.** Distance, lines in the plane, and parametric equations**Zoom Lecture 3.** Functions and graphs**Zoom Lecture 4.** Classification of functions**Zoom Lecture 5.** Limits of functions**Zoom Lecture 6.** Algebraic computation of limits**Zoom Lecture 7.** Continuity**Zoom Lecture 8.** Exponential and logarithmic functions**Zoom Lecture 9.** Problems with limits and continuity of functions**Zoom Lecture 10.** An introduction to the derivatives: Tangents**Zoom Lecture 11.** Techniques of differentiation**Zoom Lecture 12**. Differentiation of trigonometric, exponential and logarithmic functions. The chain rule**Zoom Lecture 13.** Rates of change: Modeling rectilinear motion**Zoom Lecture 14.** Implicit and logarithmic differentiation**Zoom Lecture 15.** Related rates, linear approximation, and differentials**Zoom Lecture 16.** Extreme values of continuous functions and the mean value theorem**Zoom Lecture 17.** Using derivatives to sketch the graph of a function**Zoom Review 1.** Review session for the midterm exam **Zoom Lecture 18.** Curve sketching with asymptotes: Limits involving infinity**Zoom Lecture 19.** L’Hospital rule**Zoom Lecture 20.** Optimization in physical sciences, engineering, economics and business**Zoom Lecture 21.** Antidifferentiation**Zoom Lecture 22.** Area as the limit of the sum: Riemann sums**Zoom Lecture 23.** Fundamental theorem of calculus and integration by substitution**Zoom Lecture 24.** The Mean value theorem for integrals**Zoom Lecture 25.** Numerical integration formulas**Zoom Review 2.** Review session for the final exam

## Lectures on MATH 2360-Linear Algebra, Texas Tech University-Summer 2020

This playlist collects the lectures on Linear Algebra that I taught at Texas Tech University during the Summer Term of 2020. The lectures were recorded via Zoom for online-distance teaching during the COVID-19 pandemic. They are publicly available under information on the course, and course material (with embedded, time-stamped links to the YouTube videos) can be found at https://lupucezar.wordpress.com/teaching/.**Zoom Lecture 1**. Syllabus and the big picture of linear algebra **Zoom Lecture 2.** Systems of linear equations**Zoom Lecture 3.** Matrices I**Zoom Lecture 4.** Matrices II**Zoom Lecture 5.** Determinants I**Zoom Lecture 6.** Determinants II**Zoom Review 1. **Review session for the midterm exam I**Zoom Review 2.** Review session for the midterm exam II**Zoom Lecture 7.** Vector spaces I**Zoom Lecture 8.** Vector spaces II**Zoom Lecture 9.** Vector spaces III**Zoom Lecture 10.** Vector spaces IV**Zoom Lecture 11.** Linear transformations I**Zoom Lecture 12**. Linear transformations II**Zoom Lecture 13.** Linear transformations III**Zoom Lecture 14.** Linear transformations IV**Zoom Lecture 15.** Eigenvectors and eigenvalues I**Zoom Lecture 16.** Eigenvectors and eigenvalues II**Zoom Lecture 17.** Eigenvalues and eigenvectors III**Zoom Review 3.** Review session for the final exam I**Zoom Review 4.** Review session for the final exam II**Zoom Lecture 18.** Inner product spaces I**Zoom Lecture 19.** Inner product spaces II**Zoom Lecture 20.** Inner product spaces III**Zoom Lecture 21.** Symmetric matrices and orthogonal diagonalization**Zoom Exam 1. **Midterm exam discussions and solutions

## MATH 1451-Calculus I with Applications, Fall 2020, Texas Tech University

Course description and purpose

This course introduces students to calculus, in particular, to solving problems in differentiation and integration and applying these concepts to problem solving and real world applications. This is not intended to be a course in abstract mathematics. However, some mathematical rigor, with proofs, is expected.

Students learn how to perform . Mainly, we shall cover the following topics:

**Functions and Graphs.**1.1 What is Calculus?

1.2 Preliminaries.

1.3 Lines in the plane; parametric equations.

1.4 Functions and graphs.

1.5. Inverse functions; inverse trigonometric functions.**Limits and Continuity**2.1 The limit of a function.

2.2 Algebraic computation of limits.

2.3 Continuity.

2.4 Exponential and logarithmic functions.**Differentiation.**3.1 An introduction to the derivative: tangents.

3.2 Techniques of differentiation.

3.3 Derivatives of trigonometric, exponential, and logarithmic functions.

3.4 Rates of change: modeling rectilinear motion.

3.5 The chain rule.

3.6 Implicit differentiation.

3.7 Related rates and applications.

3.8 Linear approximation and differentials.**Additional applications and derivatives and integrals.**5.1 Extreme values of a continuous function.

5.2 The mean values theorem.

5.3 Using derivatives to sketch the graph of a function.

5.4 Curve sketching with asymptotics: limits involving infinity.

5.5 L’Hospital rule.

5.6 Optimization in the physical sciences and engineering.**Integration.**4.1 Antidifferentiation.

4.2 Area as the limit of a sum.

4.3 Riemann sums and definite integrals.

4.4 The fundamental theorem of calculus.

4.5 Integration by substitution.

4.6 The mean value theorem for integrals; average value.

4.7 Numerical integration: the trapeizodal rule and Simpson’s rule.

Course number, office hours and webpage

- MATH 1351-CALCULUS I WITH APPLICATIONS, Main Campus (TTU Mechanical Engineering South Building)
- Lecturer: Cezar Lupu (Postdoctoral scholar)
- Topics covered: functions and graphs, limits of functions, continuity, differentiability and integration.
- Office hours: Tuesday & Thursday (2-3 PM), and by appointment via e-mail
- Webpage: https://lupucezar.wordpress.com/teaching/

Schedule and locations for live discussions\office hours

**Tuesday & Thursday, 2-3 PM**via Zoom (the Zoom link will be sent via email) for discussions over the materials (lecture notes, slides, and videos) sent in advance.

Policies, grading criteria, homework, exams and references

The grade will be determined by the following three factors:

*2 Gateway exams: 20% (each worth 10%)**Homework assignments (WebWork): 20%**Midterm Exam: 30%**Final exam: 30%**Attendance of review sessions: 10% (EXTRA credit!)*

All stated examinations are mandatory in order to pass the class.

Each gateway exam contains a set of 10 short questions on differentiation, respectively integration (derivatives and integrals to compute). Each gateway exam will take 30 minutes and will be scheduled by the instructor. Each gateway is administered at a unique time to the entire class – dates TBA. Procedural details will be provided in class. Midterm exams will be announced in advance in class and on my website. The final exam will take place on* Tuesday, 10.30 AM-1 PM, December 8 online via Blackboard*. The final exam is comprehensive, i.e., it will examine material from the entire course. Final exam dates are set by the university-please confirm the date of our exam on the university website.

**Grade Inquiry Policy**: Any student who has questions about any grade received on an assessment should meet with the instructor in person, if possible, within a one-week period of receiving the graded assessment. At this meeting, the instructor will provide an explanation of the grading and computation of the score. Inquires received after the one-week period will not be considered.

**Calculator**: A graphing calculator is a useful tool for this course. However, calculators or other electronic devices will NOT be permitted on quizzes, online exams, and the final exam.

**Reading**: Reading the material from the textbook (paper or electronic form) is mandatory.

**WeBWorK:** WeBWorK is an internet-based method for delivering homework problems to

students. Visit the course webpage for more information on how to access WeBWorK and how to enter your solutions; see Helpful Documents. You will need your eRaider username and student ID number with the R to log into WeBWorK. The WeBWorK system responds by telling you whether an answer (or set of answers) is correct or incorrect and also records whether you answered the question correctly or incorrectly. You are free to try a problem as many times as you wish until the due date. It is your responsibility to check WeBWorK for new assignments.

Please do not wait until the day the assignment is due to begin and/or send questions. I will not answer questions e-mailed to me within 24 hours from the HW deadline.

**Regarding the Comprehensive Final Exam**: The common final represents a course requirement.

A student who did not complete the final exam, but otherwise completed all the other requirements successfully, cannot be assigned a passing letter grade. Each designated instructor has to keep his/her copy of partial scores and grades for each student for 2 calendar years from the date of recording the grade. The final exam will be given in a proctored environment. The date for the final exam was scheduled prior to start of the semester; the location will be announced at the end of the semester. The date and time of the exam cannot be changed. Final exam conflicts may arise only between two or more math courses, in which case the course with lowest number has priority in maintaining the exam date and time.

For the final exam, students should not purchase a blue book. The exam will be distributed with on paper, with spaces to fill in/fill out. No other printed materials and electronic devices are allowed during the final. Scratch papers may be checked by the instructors.

**Make-Up Policy**: There are no make-up exams except for absence due to religious observance or absence due to officially approved trips (see Class Attendance below). The student should make arrangements to take an exam and/or quiz prior to his/her absence. In the event that an advance notice cannot be provided, the student must contact the professor within a reasonable amount of time to discuss the missed assessment.

There are no make-up WeBWorK homework sets assignments except for absence due to religious observance or absence to due officially approved trips (see Class Attendance below). If a student misses a WeBWorK homework sets for one of the above reasons, the homework set will be reopened. **Class Attendance**: Students are cautioned that active participation is necessary for success.

Attendance will be taken regularly. Students who miss no more than 1 week of classroom time during the whole semester will receive a bonus (extra credit) of 5% to their overall grade.

**During Exams, no electronic devices are allowed, including but not limited to: iPhones, smart watches, calculators of any kind, pagers. Please have all phones turned off and placed away during the classroom.**

**Letter grades** will then be assigned in accordance with the following correspondence:*Letter grade A = a percentile grade of 90% of higher**Letter grade B = a percentile grade of 80% or higher, that is lower than 90%**Letter grade C = a percentile grade of 70% or higher, that is lower than 80%**Letter grade D = a percentile grade of 60% or higher, that is lower than 70%**Letter grade F = a percentile grade lower than 60%*

The main reference include the following:

Accommodations and schedule conflicts

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both me and Student Disability Services in West Hall or call 806-742-2405, *before the end of the second week of classes*. Please see Operating Policy and Procedure 34.22 for a complete description of Texas Tech’s policy on accommodations or students with disabilities. Similarly, students who have any conflicts (including religious holy days) with the scheduled examination dates should notify me *before the end of the second week of classes*. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence.

## MATH 4000-Problem Solving for Putnam, Fall 2020, Texas Tech University

Information about the competition and seminar (course description)

The William Lowell Putnam Mathematical Competition is the premiere competition for undergraduate students in North America. More than 500 universities compete in this contest organized by the Mathematical Association of America (MAA).

### Putnam Examination (2020)

The Seventy Eight Putnam Examination will be held on **Saturday, February 20th, 2021.**

It will consist of two sessions of three hours each:

*Morning Session:*9:00am-12:00pm, location: online.*Afternoon Session:*2:00pm-5:00pm, location: online.

The test is supervised by faculty members of each participating school. Every problem is graded on a scale of 0-10. The problems are usually listed in increasing order of difficulty, with A1 and B1 the easiest, and A6 and B6 the hardest. Top 5 scoring students on the Putnam exam are named Putnam Fellows. A student can take this exam maximum four times and the Putnam official team of the university consists of 3 members. The purpose of this class is to provide a comprehensive introductioninto the world of problem solving in different branches of mathematics such as: real & complex analysis, linear algebra, abstract algebra, combinatorics, probability, geometry and trigonometry and number theory.

This course (MATH 4000-Problem Solving for Putnam) teaches important skills in problem solving that are not taught in a systematic way in any other course. These skills are extremely valuable in preparing students for jobs and for graduate-level research. The teaching style will be a mixture of a lecture and a problem-solving session. By the end of this course, students should develop fundamental problem solving skills, and become accustomed to concentrating on a problem for an extended period of time. Indeed, this seminar concentrates on the raw creative problem-solving skills which can serve as an essential ingredient in almost every field of activity.

Course number, office hours and webpage

- MATH 4000-Problem Solving for Putnam, Main Campus (Online via Zoom), Fall 2020
- Lecturer: Cezar Lupu (Postdoctoral scholar)
- Topics covered: Elementary, Abstract & Linear Algebra, Real Analysis, Combinatorics, Geometry & Trigonometry, Number Theory, Probability
- Office hours: by appointment via email
- Webpage: https://lupucezar.wordpress.com/competitions/ & https://lupucezar.wordpress.com/teaching/

Schedule and locations

**Tuesday, 12.30-1.50 PM online via Zoom (Zoom link will be sent via email)**

This is a lecture given by the instructor on a certain topic. The students will learn different concepts and techniques. Moreover, the lecturer will also present solutions of some problems and will assign other problems as homework for the students.

**Thursday,****1-1.50 PM**online via Zoom (Zoom link will be sent via email)

This is more like a recitation rather than a lecture. The 80 minutes will be divided into a problem solving time (30 minutes) to think of problems assigned prior which will be followed by a discussion of the problems (50 minutes). You don’t need to be logged in on Zoom during the problem solving time.

Syllabus, grading criteria and references

The grade will be determined by the following three factors:

*Seminar attendance: 50%**Homework and seminar activity: 50%*

Any student must attend at least 10/15 of the lectures to get full credit. Homework will be assigned *biweekly* and posted on the teaching section (https://lupucezar.wordpress.com/teaching/) of my webpage at the end of each lecture on Monday. It will consist mostly of problems of A1-B1 or A2-B2 from previous Putnam exams. The homework will be submitted as a PDF file via my email. The deadline for each homework will appear on my teaching page.

The main references include the following:

- R. Gelca, T. Andreescu, Putnam and Beyond, Springer Verlag, 2007.
- K. Kedlaya, B. Poonen, R. Vakil- The William Lowell Putnam Mathematical Competition 1985-2000: Problems, Solutions and Commentary, The Mathematical Association of America, Washington, D.C., 2002.
- L. Larson, Problem-Solving Through Problems, Springer Verlag, 1983.

**Detailed schedule (lectures & recitations)**

**Week 0.** *An invitation to the Putnam competition*

Abstract: In this lecture, we will discuss what is Putnam competition and how to train for it.

Date: August 27 (Presentation)

**Week 1.** *(Elementary) Algebra I*

Abstract: This lecture will cover problems on topics such as real algebraic identities and inequalities, and complex numbers.

Date: September 1 (Lecture), September 3 (Recitation)

**Week 2.** *(Elementary) Algebra II*

Abstract: This seminar will focus more on mathematical induction, functional equations and polynomials (integer polynomials, roots of polynomials).

Date: September 8 (Lecture), September 10 (Recitation)

**Week 3.*** Geometry and Trigonometry*

Abstract: This will cover problems on topics such as vectors, conics, quadratics, and other curves in the plane as well as trigonometric formulas.

Date: September 15 (Lecture), September 17 (Recitation)

**Week 4. ***Combinatorics*

Abstract: This will cover problems on topics combinatorial geometry, pigeonhole principle, generating functions graph theory, binomial identities and counting strategies.

Date: September 22 (Lecture) & September 24 (Recitation)

**Week 5.** *Number Theory I*

Abstract: This will cover problems on topics such as integer-valued sequences and functions, congruences, divisibility and arithmetic functions.

Date: September 29 (Lecture) & October 1 (Recitation)

**Week 6. ***Number Theory II*

Abstract: This will cover problems on topics such as quadratic residues, diophantine equations, and analytic methods in number theory.

Date: October 6 (Lecture) & October 8 (Recitation)

**Week 7. ***Abstract Algebra*

Abstract: This will cover problems on topics such as groups, rings, and finite fields.

Date: October 13 (Lecture) & October 15 (Recitation)

**Week 8. ***Linear Algebra I*

Abstract: This will cover topics on and matrices and determinants.

Date: October 20 (Lecture) & October 22 (Recitation)

**Week 9. ***Linear Algebra II*

Abstract: This will cover problems on topics such as vectors spaces, linear transformations, characteristic and minimal polynomials, eigenvalues, eigenvectors.

Date: October 27 (Lecture) & October 29 (Recitation)

**Week 10. ***Linear Algebra III*

Abstract: This will cover some special topics in linear algebra (Jordan canonical form) and beyond.

Date: November 3 (Lecture) & November 5 (Recitation)

**Week 11. ***Real Analysis I*

Abstract: This will cover problems on topics such as sequences of real numbers.

Date: November 10 (Lecture) & November 12 (Recitation)

**Week 12. ***Real Analysis II*

Abstract: This will cover problems on topics such as series of real numbers.

Date: November 17 (Lecture) & November 19 (Recitation)

**Week 13. ***Real Analysis III*

Abstract: This will cover problems on topics such as limits of functions and continuity.

Date: November 24 (Lecture)& November 26 (Recitation)

**Week 14. ***Real Analysis IV*

Abstract: This will cover problems on topics such as differentiability of functions.

Date: December 1 (Lecture) & December 3 (Recitation)

**Week 15. ***Real Analysis V*

Abstract: This will cover problems on integrability (Riemann integrals, continuity of integrals).

Date: December 8 (Lecture) & December 10 (Recitation)

**Week 16. ***Real Analysis V*I

Abstract: This will cover problems on multivariable differential and integral calculus.

Date: December 15 (Lecture) & December 17 (Recitation)

## The 2020 Math Olympiad Summer Program (MOP), July 8-28, online

The 2020 Mathematical Olympiad Summer Program will take place online via Google Meet between July 8-28. The camp is organized by the Mathematical Association of America and it is run by the CMU faculty Po-Shen Loh (director) with the help of other instructors (faculty, postdocs and Ph.D. students) from schools such as Massachusetts Institute of Technology (MIT), Stanford University, Harvard University, North Carolina State University, Carnegie Mellon University (CMU), Princeton University, Ohio State University, and Texas Tech University.

- Students will be separated into four groups.
- Black (~15 students): approx IMO gold.
- Blue (~15 students): approx IMO silver
- Green (~15 students): approx IMO bronze
- Red (~15 students): approx IMO honorable mention.

- The timetable will be (all times Eastern):
- Noon – 1:30pm (Class)
- 2:00pm – 4:00pm (Test/Quiz/Other)
- 4:00pm – 6:30pm (Test/Quiz/Other)
- 7:00pm – 8:00pm (Optional non-Olympiad seminar)
- 8:30pm – 9:00pm (Panel)

My schedule consists of 6 lectures and two seminars. More details are given below:

**Lecture 1**. *Geometric inequalities .*

Group: Black, July 9

Location: online via Google Meet

**Lecture 2**. *Algebraic integers*.

Group: Green, July 16

Location: online via Google Meet

**Lecture 3**.* Algebraic integers. *.

Group: Red, July 17

Location: online via Google Meet

**Seminar**. *Euler’s single and double zeta values.*

Group: Black, Blue, Green, Red, July 19

Location: online via Google Meet

**Lecture 4**.* **Sequences and series of real numbers and their inequalities.*

Group: Blue, July 20

Location: online via Google Meet

**Lecture 5**.* Sequences and series of real numbers and their inequalities.*

Group: Black, July 23

Location: online via Google Meet

**Lecture 6**. * Sequences and series of real numbers and their inequalities* .

Group: Green, July 24

Location: online via Google Meet

**Seminar**. *An elementary problem equivalent to the Riemann hypothesis*.

Group: Black, Blue, Green, Red , July 25

Location: online via Google Meet

## MATH 2360-Linear Algebra D-01, Summer 2020, Texas Tech University

Course description and purpose

Students learn how to perform basic vector algebra, and compute their bases, express a linear transformation as a matrix, perform basic matrix manipulations, and compute the determinant of a matrix, compute eigenvalues and eigenvectors, and use the Gram-Schmidt process. Mainly, we shall cover the following topics:

**Systems of Linear Equations.**1.1 Introduction to systems of linear equations.

1.2 Gaussian elimination and Gauss-Jordan elimination.**Matrices**2.1 Operations with matrices.

2.2 Properties of matrix operations.

2.3 The inverse of a matrix.

2.4 Elementary matrices.**Determinants**3.1 The determinant of a matrix.

3.2 Determinants and elementary operations.

3.3 Properties of determinants.**Vector Spaces**4.1 Vectors in .

4.2 Vector spaces.

4.3 Subspaces of a vector space.

4.4 Spanning sets and linear independence.

4.5 Basis and dimension.

4.6 Rank of a matrix and systems of linear equations.

4.7 Coordinates and change of basis.**Linear Transformations**6.1 Introduction to linear transformations.

6.2 The kernel and the range of a linear transformation.

6.3 Matrices for linear transformations.

6.4 Transition matrices and similarity.**Eigenvalues and Eigenvectors**7.1 Eigenvalues and eigenvectors.

7.2 Diagonalization.

Course number, office hours and webpage

- MATH 2360-Linear Algebra, Distance-Online
- Lecturer: Cezar Lupu (Postdoctoral scholar)
- Topics covered: systems of linear equations, matrices, determinants, finite-dimensional vector spaces, linear transformation, eigenvalues and eigenvectors.
- Office hours: by appointment via e-mail
- Webpage: https://lupucezar.wordpress.com/teaching/

Schedule for the Zoom online lectures

**Tuesday, 2.-3.20 PM on Zoom link provided in the email.**

**organized as follows:**

__10 OPTIONAL live lectures and a review session via Zoom, every Tuesday 2:00-3:20 PM (Central Time)__- Lecture 1 (June 2nd).
*Syllabus of the course and the big picture of linear algebra.* - Lecture 2 (June 9th).
*Systems of linear equations.* - Lecture 3 (June 16th).
*Matrices.* - Lecture 4 (June 23rd).
*Determinants*. - Lecture 5 (June 30th).
*Vector spaces I.* - Lecture 6. (July 7th).
*Vector spaces II.* - Lecture 7 (July 14th).
*Linear transformations I.* - Lecture 8 (July 21st).
*Linear transformations II.* - Lecture 9 (July 28th).
*Eigenvalues and eigenvectors I.* - Lecture 10 (August 1st)
*Eigenvalues and eigenvectors II.* **Review session for the final exam (August 4th, 6-8 PM)**.

Grading criteria, homework, exams and references

The grade will be determined by the following three factors:

- 1
*midterm exam: 30%*

*Homework assignments (WebWork): 40%**Final exam: 30%**Attendance*: 10*% (extra credit!)*

*July 2nd*. The final exam is a 24 hours take home exam and will take place on

*August 6-7*. The final exam is comprehensive, i.e., it will examine material from the entire course.

**Grade Inquiry Policy**: Any student who has questions about any grade received on an assessment should meet with the instructor in person, if possible, within a one-week period of receiving the graded assessment. At this meeting, the instructor will provide an explanation of the grading and computation of the score. Inquires received after the one-week period will not be considered.

**Reading**: Reading the material from the textbook (paper or electronic form) is mandatory.

**WeBWorK:** WeBWorK is an internet-based method for delivering homework problems to

students. Visit the course webpage for more information on how to access WeBWorK and how to enter your solutions; see Helpful Documents. You will need your eRaider username and student ID number with the R to log into WeBWorK. The WeBWorK system responds by telling you whether an answer (or set of answers) is correct or incorrect and also records whether you answered the question correctly or incorrectly. You are free to try a problem as many times as you wish until the due date. It is your responsibility to check WeBWorK for new assignments.

Please do not wait until the day the assignment is due to begin and/or send questions. I will not answer questions e-mailed to me within 24 hours from the HW deadline.

**Regarding the Comprehensive Final Exam**: The final represents a course requirement. A student who did not complete the final exam, but otherwise completed all the other

requirements successfully, cannot be assigned a passing letter grade. Each designated

instructor has to keep his/her copy of partial scores and grades for each student for 2 calendar years from the date of recording the grade. The final exam will be given in a proctored environment. The date for the final exam was scheduled prior to start of the semester; the location will be announced at the end of the semester. The date and time of the exam cannot be changed. Final exam conflicts may arise only between two or more math courses, in which case the course with lowest number has priority in maintaining the exam date and time.

For the final exam, students should not purchase a blue book. The exam will be distributed with on paper, with spaces to fill in/fill out. No other printed materials and electronic devices are allowed during the final. Scratch papers may be checked by the instructors.

**Make-Up Policy**: There are no make-up exams except for absence due to religious observance or absence due to officially approved trips (see Class Attendance below). The student should make arrangements to take an exam and/or quiz prior to his/her absence. In the event that an advance notice cannot be provided, the student must contact the professor within a reasonable amount of time to discuss the missed assessment.

There are no make-up WeBWorK homework sets assignments except for absence due to religious observance or absence to due officially approved trips (see Class Attendance below). If a student misses a WeBWorK homework sets for one of the above reasons, the homework set will be reopened.

**Class Attendance**: Students are cautioned that active participation is necessary for success.

Attendance will be taken regularly. Students who miss no more than 2 weeks of classroom time during the whole semester will receive a bonus (extra credit) of 10% to their overall grade.

* *Letter grades will then be assigned in accordance with the following correspondence:

*Letter grade A = a percentile grade of 90% of higher*

*Letter grade B = a percentile grade of 80% or higher, that is lower than 90%*

*Letter grade C = a percentile grade of 70% or higher, that is lower than 80%*

*Letter grade D = a percentile grade of 60% or higher, that is lower than 70%*

*Letter grade F = a percentile grade lower than 60%*

The main references include the following:

- Ron Larson, Elementary Linear Algebra (8th edition), published by Cengage.
- Sergei Treil, Linear Algebra Done Wrong, published by Brown University.
- Tom Denton, Andrew Waldron, Linear Algebra in Twenty Five Lectures, UC Davis course.
- Gilbert Strang, Introduction to Linear Algebra, MIT course.

Accommodations and schedule conflicts

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both me and Student Disability Services in West Hall or call 806-742-2405, * before the end of the second week of classes*. Please see Operating Policy and Procedure 34.22 for a complete description of Texas Tech’s policy on accommodations or students with disabilities. Similarly, students who have any conflicts (including religious holy days) with the scheduled examination dates should notify me *before the end of the second week of classes*. A student who is absent from classes for the observance of a religious holy day shall be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence.