General Information

      Instructor: Dave Rusin ( 
      Office hrs: I will be in my office (RLM 9.140) at these times for you:
         Mondays and Wednesdays 1-2 pm and 3-4pm
         Fridays 9:30-11 am and 1-2 pm.
      I will hold additional office hours near exam times, and can also
      be available by appointment; talk to me or send email to arrange it.

UPDATE: I will keep the same office hours through Zoom. Those meetings are open to all; if you need to speak to me privately (e.g. to discuss a grade or personal issue) please send an email and I will arrange a time to meet you privately (by Zoom, phone, skype, etc.) Here is the invitation to the MWF 1pm office hour: and the 3pm OH: Text: Elementary Number Theory and its Applications (Rosen, 6th edition) This course has Unique ID 52886 and meets MWF at 2pm in ECJ 1.306 ,

UPDATE: We will convene at the same time by Zoom. Those class meetings will be recorded and uploaded to YouTube. The URL for the class meeting us The meetings will be recorded and loaded to YouTube : Registration in this course is closed; I can't put anyone into it. If you think you will probably drop the course, please do so promptly and allow another student to take your place. Your final exam will be held Thursday, May 14, 2:00 pm--5:00 pm There is no provision for taking the final exam earlier or later. You can always confirm your own exam schedule at the Registrar's web site. The exam may not be held in the regular classroom; I will announce the location when I know it.

UPDATE: Here is the FINAL EXAM and here is an answer key with extra comments

Course webpage: It is unlikely that I will post any important material to Canvas; for any additional information I want to give you outside of class you should come to this webpage.

I showed you guys a Number Theory web page on Friday and you asked for a link. The best I can offer you is to use the Wayback Machine because the web site has gone offline. Here is a reasonable starting point for the Mathematical Atlas

I advertised office hours for Monday May 11; use this zoom invitation:

The final exam will be available by 9am on Wednesday May 13 and is due Friday May 15 by 11:59pm. I will send email when it is ready.

I promised I would put online the homework I announced in class. Here is a separate web page that lists the written homework I am asking you to turn in.

I'd like to meet with each of you on zoom at these times

Course Description

Number Theory is the study of the properties of the integers and related constructs. We will look at primes and squares and so on, which you have probably known about for years, but watch out! This course progresses very far and fast and you will learn some amazing things about the integers. For example, I will show you how a very large portion of Internet security works, and tell you how you may crack it.

This is a first course that emphasizes understanding and creating proofs; therefore, it must provide a transition from the problem-solving approach of calculus to the entirely rigorous approach of advanced courses such as M365C or M373K. The number of topics required for coverage has been kept modest so as to allow instructors adequate time to concentrate on developing the students theorem-proving skills.


M341 or M325K, with a grade of at least C-.

Class structure

I would like to use our very limited time together to be more productive by getting you to do things rather than sit passively listening to me drone on and on. When we are learning something algorithmic, I may stop and ask you to work out some examples; I'll come around the room to see how you're doing. When we're learning more about the theory, I will ask you to provide steps of a proof, or to think of counterexample, etc. Let's make the class sessions productive!

Graded material

Homeworks: I intend to assign homework problems approximately weekly. By all means work with your friends but you must write up your own work.

UPDATE: You will have to submit your homework electronically via Canvas. Handwritten and scanned submissions are fine but I also encourage you to investigate TeX (LaTeX), which is what all mathematicians use to get mathematics typed and printed. Time invested in this now will pay off in your mathematical career!

I will drop the two lowest homework grades and average the rest to give you a "Homework Score" of up to 100 points for the semester Homework scores will then be converted to letter grades using the following scale:

Exams: There will be 2 mid-term exams, to be held during the usual class period, and a comprehensive final exam. Midterm 2 is now posted at

UPDATE: The second midterm will be a take-home exam. I will schedule a 15-minute "office hour" with each of you to take place shortly after the exam, during which we will talk about your exam answers. Yes, this is an attempt to control for cheating but it will also be a good teaching moment that I think will serve you well!

I will use the scale above to convert your exam raw score to a letter grade, but because my exams tend to be hard, I will also use the following alternative method if it gives you a higher letter grade. After I compute the mean and the standard deviation of the class grades, I will determine how many standard deviations above or below the mean your grade is. If your score is greater than the mean by less than one standard deviation, you will get a B (or B+ or B-, as appropriate); higher scores get A's, lower scores get C's, D's, and F's. For example, suppose the class average on the exam was 78.3 points and the standard deviation was 14.4 points. Then the conversion from raw scores to letter grades will be based on these brackets (of width 14.4/3 = 4.8 up and down from 78.3) :
98+ A+
In this way I am literally giving grades of "above average" (A's and B's) exactly to students whose scores are above the class average. (Mean is not the same as median; most of my students last semester got A's and B's; only a few of the letter grades were D's and F's.)

Letter Grades

Your final semester grade is simply a weighted average of the components: homework 30%, midterms 20% each, and the final exam 30%. I do the arithmetic as is done for high-school GPAs: A=4.0, B=3.0, etc; "+" and "-" are one-third of a letter grade up or down. An average of 3.83 rounds down to an A- (3.67) while 3.84 rounds up to an A (4.00), etc. Sadly, the university does not permit me to report scores of "A+" but internally I do track those terrific students whose semester average is 4.17 or above!


Classroom activity: Our meeting times together are very short so we must make the most of them. Come to class daily and ask questions; this is greatly facilitated by reading ahead each day and doing the homework problems as they are assigned. Please silence your cell phones. I will always assume that any talking I hear is about the course material so I may ask you to share your conversations with the class.

Make-ups: It is in general not possible to make up missing homework assignments after the due date. If you believe you will have to miss a graded event, please notify me in advance; I will try to arrange for you to complete the work early.

Students with disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.

Religious holidays: If you are unable to participate in a required class activity (such as an exam) because it conflicts with your religious traditions, please notify me IN ADVANCE and I will make accommodations for you. Typically I will ask you to complete the required work before the religious observance begins.

Academic Integrity. Please read the message about Academic Integrity from the Dean of Students Office. I very much prefer to treat you as professionals whose honesty is beyond question; but if my trust is violated I will follow the procedures available to me to see that dishonesty is exposed and punished.

Campus safety: Please familiarize yourself with the Emergency Preparedness instructions provided by the university's Campus Safety and Security office. In the event of severe weather or a security threat, we will immediately suspend class and follow the instructions given. You may wish to sign up with the campus alert programs.

Counseling: Students often encounter non-academic difficulties during the semester, including stresses from family, health issues, and lifestyle choices. I am not trained to help you with these but do encourage you to take advantage of the Counselling and Mental Health Center, Student Services Bldg (SSB), 5th Floor, open M-F 8am-5pm. (512 471 3515, or

Drop dates: Jan 2 is the last day to drop without approval of the department chair; Feb 5 is the last day to drop the course for a possible refund; Apr 6 is the last day an undergraduate student may, with the dean's approval, withdraw from the University or drop a class except for urgent and substantiated, nonacademic reasons. For more information about deadlines for adding and dropping the course under different circumstances, please consult the Registrar's web page,

UPDATE: Please note that the Deans are extending the deadlines during which you may Q-drop the course or change from graded- to pass-fail options. Please consult with me or an academic advisor to determine the most up-to-date rules. The University wants you to have the fullest possible educational experience but recognizes that current circumstances may force students to make unexpected enrollment decisions.

Computers: Some topics in this course are very well suited to numerical experiments beyond the range of what you can do with pencil and paper. I encourage you to try the biggest and most informative examples you can. You are welcome to use the department's computer facilities. Our 40-seat undergrad computer lab in RLM 7.122, is open to all students enrolled in Math courses. Students can sign up for an individual account themselves in the computer lab using their UT EID. We have most of the mainstream commercial math software: Mathematica, Maple, Matlab, etc., and an assortment of open source programs. If you come to my office you will see me use some of this software to help illustrate concepts. Please see me if you would like more information.

UPDATE: Sadly the computer lab is shuttered for now. Still, Number Theory lends itself well to computer exploration so if you have some programming skill and would like to try some projects I can work with you individually.


Here is a rough approximation to the timetable of topics, but I reserve the right to adjust this to meet the needs and interests of the class. Let me know what you would like to learn about!

UPDATE: Now more than ever it would be helpful for you to tell me what interests you. My default plan will be to push back the syllabus by one week and, sadly, skip Chapter 13. I welcome your input as the semester progresses.