Number Theory is the study of arithmetic properties of numbers. Prime numbers are of gret importance in Number Theory, as they are the building blocks for integers. Several applications in technology and security rely on number theoretical properties.
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COMMUNICATION
Messages and announcements will be done using Canvas. When you need to contact your instructor or TA, please use Canvas as email messages will NOT be replied. This is to make communication more efficient, so we can correctly identify your section and other important information.
We will use Piazza for questions regarding HW, exams, lectures, etc. This tool is great for collaboration and to write math. It is difficult to type math in an email or in Canvas, so use Piazza for all content related questions!
If you have any questions, don't forget to go office hours.
Pedro Morales:
M,W 9:30-11:00am
McHenry 4120
Phillip Barron:
M: 3:45-5:15 pm, Th: 12:00 - 1:30 pm
McHenry 1261
For anything else, you can reach your instructor or TA using email, but please use this as the LAST method of communication.
Grade
Grades will be assigned using the +/- system.
Homework and Classwork (50%)
Pre-Class (8%)
These are short assignments and reflections that you will complete on Canvas.
We are dropping the lowest 5 preclass in order to account for any abscences.
In-Class (8%)
We will have group Activities during lecture time. You will have a different group every week. Group numbers for each week can be checked in Canvas. The Activities are applications of the concepts seen in class.
We are dropping the lowest 2 inclass Activities in order to account for any abscences.
Post-Class (10%)
Each week, I will assign homework problems. Every Friday during class, you will be asked to copy and turn in the solutions for three homework problems. You will keep the rest of the homework to study and practice.
We are dropping the lowest 2 postclass in order to account for any abscences.
Section (9%)
Each Section day you will have different explorations or activities to work on. Every week you will be assigned a group number that you can check on Canvas. The explorations or activities will be completed on Canvas, so make sure every member of the group brings a computer or handheld device. Participation and attendance will be counted towards the Section grade.
We are dropping the lowest 2 section grades in order to account for any abscences.
Book report (15%)
We will have a book report over the book:
The Music of the Primes
by Marcus du Sautoy
The report will consist in three parts
Exams (50%)
No calculators allowed at any Exams. No makeup exams under any circumstances. Under a valid emergency, one absence could be replaced by the final.
Midterms (30%)
These exams cover the class material. The grade is computed by averaging the exams in the regular fashion.
Midterms will take place during lecture time.
Exam 1
February 1st
Exam 2
March 1st
Final (20%)
The final is comprehensive.
Final
March 21st
4:00-7:00pm
Responsibility (+)
This measures your responsibility, consistency, and engagement with the course. It is computed with your Pre-Class, Section, Activities, Reflections, and participation in SGT sessions and ACE sessions. This can give you a boost of at most 5 pts in your final grade.
The boost is computed by, $$5\beta\,,$$ where $\beta$is the significance level for the hypothesis that the variance of grades is less than $\sigma_0$, $$\chi^2_\beta=n\left(\frac{\sigma_x}{\sigma_0}\right)^2\,,$$ with $\chi^2$ the Chi-square distribution, $n$ the number of assignments and $\sigma_x$ the standard deviation of the assingments.
Prerequisite and degree relevance
Prime numbers, unique factorization, congruences with applications (e.g., to magic squares). Rational and irrational numbers. Continued fractions. Introduction to Diophantine equations. An introduction to some of the ideas and outstanding problems of modern mathematics.
Prerequisite(s): course 100 or Computer Science 101.
The UC Santa Cruz community includes students, staff, faculty, and others who have a vested interest in the University. As members of an academic community, integrity, accountability and mutual respect are vital pillars of being part of this community. The Principles of Community further illustrate the values and expectations set forth for being a part of this community.
Small Group Tutoring provides a small interactive setting for students to be comfortable to engage in conversations about course material with other students. Each session is led by a current UCSC undergraduate student who has taken the course and done well in it. Tutoring sessions are 1-Hour long and generally have a capacity of 6 students. When students sign up for tutoring, students make a commitment to attend tutoring weekly for the entire quarter. All students can sign up for up to 2-Hours of tutoring a week per couse they are enrolled in.
ACE is an academic support program dedicated to increasing the diversity of UCSC students earning bachelors' degrees in science, technology, engineering, and mathematics. It is a community of scholars who strive for and commit to academic excellence.
UC Santa Cruz is committed to creating an academic environment that supports its diverse student body. If you are a student with a disability who requires accommodations to achieve equal access in this course, please submit your Accommodation Authorization Letter from the Disability Resource Center (DRC) to me privately during my office hours or by appointment, preferably within the first two weeks of the quarter. At that time, I would also like us to discuss ways we can ensure your full participation in the course. I encourage all students who may benefit from learning more about DRC services to contact DRC by phone at 831-459-2089 or by email at drc@ucsc.edu.
We understand that our members represent a rich variety of backgrounds and perspectives. UCSC is committed to providing an atmosphere for learning that respects diversity. While working together to build this community we ask all members to:
FAQ
Is the book required for the class?
No. The book is a good reference to clarify concepts and to practice more problems.
Was there a curve last semester?
No. We don't do curves in this class.
I am going to miss a day of class. What should I do?
Get the notes from someone in class. You can also see what are we going to do that day by looking at the lecture schedule.
Can we use calculators on the Exams?
No.
This Homework problem is impossible to do without a calculator. What should I do if it's on the Exam?
If a Homework problem really is impossible to do without a calculator, it won't be on the Exam.
I have class all the way over on the other side of campus before your class. Can I come in a few minutes late?
Yes, just be courteous to your classmates and be as quiet as possible when you come in.
What can I do to improve my grade?
Study. Do Homework. Do not wait until the end of the semester.
Do you drop any grades?
See the grade description.
I need a C to keep my scholarship, what can I do?
Study. Do Homework. Do not wait until the end of the semester.
I added this class late and missed the first one/two/three Homeworks. Can you accept them late?
No. We do not accept late Homework for any reason. Your two lowest Homework scores are dropped for just such eventualities.
Will there be a curve?
No.
What do I have to make on the final to get an A/B/C in the course?
We use the regular grading system.
I sent a math question to my instructor and I didn't get a response. Why?
Because it's impossible to write math over e-mail.
Can we use calculators on the Homeworks?
Yes.
Do we have to bring our textbooks to class everyday?
No.
I have a doctor's appointment after class today. Can I leave a few minutes early?
Yes, just be courteous to your classmates and be as quiet as possible when you leave.
Do you give extra credit?
No but we have grade boosts based on your performance in class.
What is going to be on the exam?
Everything we have done in class.
Why you don’t reply my emails?
Messages regarding this class must be sent through Canvas or Piazza.