Math 106
Algebra and Number Theory 1
Faculty
Laurent Cantier
Post-Doctoral Fellow at Universitat Autònoma de Barcelona
Course length
Duration
Total hours
Credits
Language
Course type
Fee for single course
Fee for degree students
Skills you’ll learn
Overview
Students will learn about basic notions of Number Theory, such as congruences, prime numbers, Euclidean algorithm and arithmetic/geometric sequences. As an application, they will be introduced to Cryptography.
Learning highlights
- The main objective of this course is to refresh basic notions of Algebra from highschool and deepen into the Number Theory, that will allow the student to get an introductive view on cryptography and its relation to prime numbers.
- Ratios – Congruences - Prime Numbers – Study of sequences – Cryptography.
Course outline
15 classes
Session 1
Ratios and Conversion Factors
Session 2
Percent
Session 3
Proportions
Session 4
Rate Problems
Session 5
Arithmetic Sequences
Session 6
Review + Midterm 1
Session 7
Geometric Sequences
Session 8
Prime Numbers
Session 9
Division Algorithm
Session 10
Congruence
Session 11
Review + Midterm 2 + Application to Cryptography
Session 12
Euclidean Algorithm
Session 13
Integer Representations
Session 14
Overall Review + Application to Cryptography
Final Exam
Final Exam
Course materials
Books
Methodology
Each class will be divided into a theoretical part given by the professor, followed by a practical session, where students will solve problems related to what has been presented, under the professor’s supervision.
There will be room for open discussion and questions. Training and exercises will be recommended after each class. Also at the end of each week, an assignment will be given to hand over to the professor on the following Monday.
Finally, 2 Midterms exams (on Mondays) and a final exam on the last day will complete the grade of the student. Participation is more than welcome, and will be part of the final grade also.
Grading
Laurent graduated from Grande Ecole Centrale de Nantes in France, and then obtained his PhD in Mathematics at the Universitat Autònoma de Barcelona (UAB) in 2020.
After a first post-doctoral position at the UAB, he was awarded a three-year Margarita Salas grant in January 2022. He is currently co-hosted as a postdoctoral fellow at the Institute of Mathematics of the Czech Academy of Sciences (IMCAS) and the UAB.
See full profileApply for this course
Algebra and Number Theory 1
by Laurent Cantier
Total hours
45 Hours
Dates
Jan 31 - Feb 18, 2022
Fee for single course
€1500
Fee for degree students
€750
How to secure your spot
Complete the form below to kickstart your application
Schedule your Harbour.Space interview
If successful, get ready to join us on campus
FAQ
Will I receive a certificate after completion?
Yes. Upon completion of the course, you will receive a certificate signed by the director of the program your course belonged to.
Do I need a visa?
This depends on your case. Please check with the Spanish or Thai consulate in your country of residence about visa requirements. We will do our part to provide you with the necessary documents, such as the Certificate of Enrollment.
Can I get a discount?
Yes. The easiest way to enroll in a course at a discounted price is to register for multiple courses. Registering for multiple courses will reduce the cost per individual course. Please ask the Admissions Office for more information about the other kinds of discounts we offer and what you can do to receive one.