47 results authored by Daniel Mansfield - search across all users.

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• Question

Introduces the GCD and a simple form of the Euclidian Algorithm

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Gentle intro to modular arithmetic through quotients and remainders

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Introduction to modular arithmetic using a multiplication table and lookup.

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Full worked solution using the Extended Euclidian Algorithm

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Introduction to modular arithmetic in $\mathbb Z_b$ using a multiplication table and lookup with coprime $b \in \mathbb N$.

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Simple counting exercise, with combinations

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Introduction to counting with permutations and combinations

• Recurrence: second order
Needs to be tested
Question

How to find solutions to a second order recurrence relation.

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Introduction to first order recurrence relations with a simple example, including homogenous and non-homogenous solutions.

• Question

No description given

• Question

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Question

Quadratic factorisation that does not rely upon pattern matching.

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• Question

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Couting application where repitition is allowed and order does not matter.

• Counting 2: a deck of cards
Needs to be tested
Question

Applicaiton of the pigeonhole principle

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Definition of the pigeonhole principle, and some examples

• Counting by cases
Needs to be tested
Question

Simple counting exercise. Students are encouraged to look for the smart way of counting.

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English sentences are given and for each the appropriate proposition involving quantifiers is to be chosen. Also choose whether the propositions are true or false.

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English sentences which are propositions are given and for each the appropriate proposition  involving quantifiers is to be chosen.

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English sentences which are propositions are given and the appropriate logical expression chosen for the negation of the sentence.

• Strong Induction
Needs to be tested
Question

Intorduces strong induction and uses it to verify the solutions of a second order linear recurrence.

• Question

No description given

• Proof 1: even and odd integers
Needs to be tested
Question

Intorduction to using the defnition to prove simple stamtements.

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Intorduction to proof and existence statements.

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Simple intro to mod arithmetic

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Intorduces students to the definition of a function $f:A\mapsto B$ as a subset of the Cartesian product $A\times B$.

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Slightly harder introductory exercises about the power set.

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Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

• Exam (7 questions)

Formative assessment to introduce the concepts of modular arithmetic.