MA163 Mathematics
Delivered:

Semester I

Credits:

5 ECTS

Examined:

Semester I

Exam duration:

2 hours

No. lectures:

48

No. tutorials:

12

CA

6 online homeworks

Exam weighting:

100%

CA weighting:

0%

Syllabus & Learning Outcomes

1: Elementary Number Theory
Syllabus
 Modular arithmetic, Euclidean algorithm,
applications to ISBNs and cryptography
 Euler's Phi function, Fermat's little theorem (and its proof),
application to public key cryptography
 Chinese Remainder Theorem
Learning outcomes
 You will be able to use modular arithmetic and Euler's Phi function to: detect errors in ISBNs; encipher messages using 1dimensional affine and RSA cryptosystems; attack 1dimensional affine cryptosystems; calculate with Chinese remainders. You will also be able to present a proof of Fermat's little theorem.

2: Matrix arithmetic
Syllabus
 Matrix addition, multiplication, row operations, inversion (via row operations), systems of
equations, applications to resource allocation problems
 Linear transformations, applications to cryptography
and geometry
Learning outcomes
 You will be able to use matrices to: solve resource allocation problems; encipher messages using higher dimensional affine cryptosystems; attack higher dimensional affine cryptosystems; solve some geometric problems.

3: Eigenvalues and eigenvectors
Syllabus
 Calculation of eigenvalues, eigenvectors and matrix
powers for 2x2 matrices, HamiltonCayley theorem (with proof for 2x2 matrices)
 Proof by induction
 Fibonacci sequence, Golden Ratio, applications to practical
recurrence problems
Learning outcomes
 You will be able to use eigenvalues, eigenvectors and the Principle of Induction to solve practical and theoretical problems about recurrence. You will also be able to state the HamiltonCayley theorem and prove it in the 2x2 case.
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