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Level 4 Diploma in Cyber Security

Proof techniques: induction and strong induction, contradiction, cases, counterexamples, pigeonhole principle

CYB402 · Mathematics for Computer Science — Week 5 of 16

CourseCYB402
Week5 of 16
SemesterI
TutorOnline in the course chat

This week’s topics

Proof techniques: induction and strong induction, contradiction, cases, counterexamples, pigeonhole principle

  1. Proof techniques: induction and strong induction, contradiction, cases, counterexamples, pigeonhole principle
  2. Choosing an appropriate proof

What you will be able to do

  • 2.1 Describe a range of mathematical proof techniques.
  • 2.6 Evaluate mathematical proof techniques and the circumstances under which they may be appropriate.

Activity

Seminar, guided reading and a short written task: describe a range of mathematical proof techniques.

Study materials

The teaching notes, exercises and videos of this week are in the student portal. Your portal is set up as soon as you receive final acceptance, so you can open them before the semester starts.
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Course chat

Admitted students ask questions on this week’s page in the student portal: an AI assistant trained on the course answers first, and during the course’s timetabled classes Connect to your tutor brings your tutor into the chat, who may start a call if needed.

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Course plan
  • Week 1: Number bases: binary, denary and hexadecimal, and convertin…
  • Week 2: Binary in computer science: binary addition and overflow, t…
  • Week 3: Propositional logic: Boolean operators and truth tables
  • Week 4: Set theory: Venn diagrams, notation, union, intersection an…
  • Week 5: Proof techniques: induction and strong induction, contradic…
  • Week 6: Finite fields and modular arithmetic: algebras, identities …
  • Week 7: Number-theoretic theorems (Fermat's little theorem, Euler's…
  • Midterm: Midterm evaluation
  • Week 9: Sequences and series: arithmetic, geometric and harmonic pr…
  • Week 10: Vectors and matrices: matrix multiplication, inverses and s…
  • Week 11: Matrix types and properties (trace, determinant), LU decomp…
  • Week 12: Applying Mathematics for Computer Science in practice: case…
  • Week 13: Assignment workshop: research, planning and referencing
  • Week 14: Assignment workshop: drafting, feedback and improvement
  • Week 15: Review and coursework completion
  • Final: Final assessment and submission
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