47 results authored by Daniel Mansfield  search across all users.

Question in Discrete Mathematics
Introduces the GCD and a simple form of the Euclidian Algorithm

Question in Discrete Mathematics
Gentle intro to modular arithmetic through quotients and remainders

Question in Discrete Mathematics
Introduction to modular arithmetic using a multiplication table and lookup.

Question in Discrete Mathematics
Full worked solution using the Extended Euclidian Algorithm

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

Question in Discrete Mathematics
Simple counting exercise, with combinations

Question in Discrete Mathematics
Introduction to counting with permutations and combinations

Question in Discrete Mathematics
How to find solutions to a second order recurrence relation.

Question in Discrete Mathematics
Introduction to first order recurrence relations with a simple example, including homogenous and nonhomogenous solutions.

Question in Discrete Mathematics
No description given

Question in Fundamentals of Mathematics
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 in Fundamentals of Mathematics
Quadratic factorisation that does not rely upon pattern matching.

Question in Discrete Mathematics
Introductory exercise about power sets.

Question in Discrete Mathematics
Introductory exercise about subsets using custom grading code.

Question in Discrete Mathematics
Couting application where repitition is allowed and order does not matter.

Question in Discrete Mathematics
Applicaiton of the pigeonhole principle

Question in Discrete Mathematics
Definition of the pigeonhole principle, and some examples

Question in Discrete Mathematics
Simple counting exercise. Students are encouraged to look for the smart way of counting.

Question in Discrete Mathematics
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.

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

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

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

Question in Discrete Mathematics
No description given

Question in Discrete Mathematics
Intorduction to using the defnition to prove simple stamtements.

Question in Discrete Mathematics
Intorduction to proof and existence statements.

Question in Discrete Mathematics
Simple intro to mod arithmetic

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

Question in Discrete Mathematics
Slightly harder introductory exercises about the power set.

Question in Discrete Mathematics
Simple exercises introducing the fundamental set operations, and NUMBAS syntax for sets.

Exam (7 questions) in Discrete Mathematics
Formative assessment to introduce the concepts of modular arithmetic.