The Magic of Numbers

University of Toronto Scarborough

A selection from the following topics: the number sense (neuroscience of numbers); numerical notation in different cultures; what is a number; Zeno's paradox; divisibility, the fascination of prime numbers; prime numbers and encryption; perspective in art and geometry; Kepler and platonic solids; golden mean, Fibonacci sequence; elementary probability.
More Less

24HR Notes for MATA02H3

Available 24 hours after each lecture

Sophie Chrysostomou

Current Lecture
MATA02H3 Lecture Notes - Winter 2019, Lecture 12 - Modular Arithmetic, Euclidean Algorithm, Multiplication Table

MATA02 - Lecture 12 - Solving Modular Arithmetic Problems, Euclidean Algorithm, Modular Properties (February 13th, 2019) Multiplication Table for Module 6 X 0 1 2 3 4 5 0 0 0 0 0 0 0 1 0 1 2 3 4 5 2 0 2 4 0 2 4 3 0 3 0 3 0...

Sophie Chrysostomou
Next Lecture
Coming Soon

Available as soon as 21 Feb 2019

Sophie Chrysostomou

MATA02H3 Syllabus for Sophie Chrysostomou — Winter 2019

MATA02-The Magic of Numbers
DESCRIPTION: This course is intended for students with no background in mathe-
matics beyond grade 10. The course will explore what numbers are. We will follow a path
which begins with divisibility and leads to the fascinating topic of prime numbers and their
mysteries. The course will study a striking application, RSA encryption. This is the form
of encryption generally used to secure transactions on the internet. We will go on to look at
rational numbers and real numbers. This will force us to consider what we mean by saying
that these are “infinite” sets of numbers, and why there are “more” real numbers than ra-
tional numbers.
ADMINISTRIVIA: Instructor: Sophie Chrysostomou
Office: IC 476, Office Hours: TBA
Note: You must use your University of Toronto email to contact the instructor.
Be sure to include the course code as part of the subject line and sign the email
with your first and last name, as well as your student ID.
TOPICS: What is a number? Numbers and lengths, visualizing numbers on the num-
ber line; Divisibility, Euclidean algorithm; Clock arithmetic: congruences; Divisibility tests;
Prime numbers: Eratosthenes sieve, how many are there, how are they distributed; RSA
encryption; Rational numbers, real numbers.
The Magic of Numbers, Gross and Harris, Chapters 8-22, available in pdf form on
Supplemental examples and homework material will be posted.
Assignments (5 in total): 15% due on Wednesdays of the weeks 3, 5, 7, 9, 11.
Quizzes (5 in total): 15% in tutorials during the weeks 4, 6, 8, 10, 12.
Term Test: 30%
Final Exam: 40%
POLICY ON MISSING QUIZZES: Should you miss a quiz due to a legitimate reason,
a make up quiz will be provided. In order to qualify to write it: (a) you must notify the
coordinator of the course by email no later than 48 hours from the ending of the missed quiz
and (b) you must submit appropriate documentation within 4 days of the missed quiz. If
the reason is medical, an official UTSC medical form should be used. Failure to follow (a)
or (b) as stated in this paragraph will result in a grade of zero for that quiz.
POLICY ON MISSING THE TEST: If you miss the midterm test because of the
following reasons: severe illness, injury or accident, family catastrophe, religious obligations,
or legal obligations, you must (a) notify Sophie Chrysostomou by email no later than 48
hours from the ending of the test and (b) submit to her appropriate documentation within
4 days of the missed test documenting and validating the reason for missing the test. If
the reason is medical, an official UTSC medical form should be used. A scanned copy of
the medical note should be sent to Sophie Chrysostomou by email within 4 days from the
missed test. Once able to attend classes, the original note should be submitted to her as
well. Failure to follow (a) or (b) as stated in this paragraph will result in a grade of zero for
that test.
The following reasons will not be considered for any sort of compensation for missing the
midterm test: work obligations, vacation leave, being out of country, extra-curricular activ-
ities such as sports or clubs, slight illness, misreading the time of day or location, lateness,
timetable or other test conflict, other course conflicts, traffic or other transportation issues.
CALCULATORS: For this course, you will need to have a standard hand-held calcu-
lator with no capacity to store text. If need be, you can ask your TA or instructor if your
calculator is approved to be used on the test. You will be allowed ONE such calculator
during the writing of midterm test and final examination. All other electronic devices are
prohibited on midterm test and final examination.
ACCESSIBILITY: Students with diverse learning styles and needs are welcome in this
course. In particular, if you have a disability/health consideration that may require accom-
modations, please feel free to approach me and/or the AccessAbility Services Office as soon
as possible. I will work with you and AccessAbility Services to ensure you can achieve your
learning goals in this course. Enquiries are confidential. The UTSC AccessAbility Services
staff are available by appointment to assess specific needs, provide referrals and arrange ap-
propriate accommodations (416) 287-7560 or
Academic integrity is essential to the pursuit of learning and scholarship in a university,
and to ensuring that a degree from the University of Toronto is a strong signal of each stu-
dent’s individual academic achievement. As a result, the University treats cases of cheating
very seriously. The University of Toronto’s Code of Behaviour on Academic Matters outlines
the behaviours that constitute academic dishonesty and consequences of academic offences at:
Potential offences include, but are not limited to misrepresenting your identity, using or pos-
sessing unauthorized aids, looking at someone elses answers during an exam, test or quiz, us-
ing someone else’s ideas or words without appropriate acknowledgement, making up sources
or facts etc.
All suspected cases of academic dishonesty will be investigated following procedures
outlined in the Code of Behaviour on Academic Matters. For more info please go to

Log In


Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.