Unit 11: Maths for Computing
Student Name/ID
Number
Unit Number and Title
11: Maths for Computing
Academic Year
Unit Tutor
Assignment Title
Calculus
Issue Date
Submission Date
IV Name & Date
Submission Format
Part 1: Written report
Part 2: Seminar paper
Part 3: Written report
Part 4: Written report
Unit Learning Outcomes
LO1 Use applied number theory in practical computing scenarios
LO2 Analyse events using probability theory and probability distributions
LO3 Determine solutions of graphical examples using geometry and vector methods
LO4 Evaluate problems concerning differential and integral calculus
Assignment Brief and Guidance
Activity
Part 1
(LO1)
Research the importance of prime numbers in different areas of computing. Explore various
types of primes (for instance, Mersenne Primes) used in the field, why and how they are used. As
part of your report, show how LCM, GCF, series and sequences, and multiplicative inverses can be
used to prove your findings. Also demonstrate how binary outputs can be converted into more
easily understandable information for users.
Part 2 (LO2)
You have been asked to produce a seminar paper on probability theory and probability
distributions. Within the paper, there should be three sections that provide opportunities to
showcase examples and calculations supporting both theory and distribution elements.
One section should be assigned to a practical example that you have chosen to illustrate probability
theory, hashing and balancing. You have selected network traffic as a practical scenario, as it can be
broadly classified into the following categories:
1.
Busy/heavy traffic – High bandwidth is consumed in this traffic
2.
Non-real-time traffic – Consumption of bandwidth during working hours
3.
Interactive traffic – Is subject to competition for bandwidth and could result in poor
response times if prioritisation of applications and traffic is not set
4.
Latency-sensitive traffic – Is subject to competition for bandwidth and could result in
poor response times
Using this example, evaluate probability theory in relation to hashing and load balancing,taking into
consideration traffic categories.
The second section will focus on deducing the conditional probability of different eventsoccurring
within independent trials.
You are required to introduce the concept/expectation of an event occurring from a discrete,
random variable. You could link this into the network traffic example in terms ofnumber of
counts, for example the amount of downtime over a certain period or provideanother example
to showcase this. In addition, identify the expectation of an event occurring from a discrete,
random variable.
The final section should provide calculative examples of probabilities within both binomially
distributed and normally distributed random variables.
Part 3 (LO3)
Given the following cartesian co-ordinates; A=(0,10), B=(10,0), C=(10,10), D=(0,0), E=(5,10),F=(5,0); we are
given four simple shapes; ACBD, AEFD, DBC, ACF.
Identify the shapes, then define their parameters using appropriate vector methods andshow how
vector co-ordinates are used to scale them.
Research the co-ordinate system used in programming a simple output and evaluate it.
Part 4 (LO4)
Rates of change are used daily in life and include but are not limited to: the performance of
individuals against a benchmark such as ability, strength in a sporting environment, achievements in
terms of exam results, temperature in relation to time of day, rates of growth or changes in stock
levels etc.
Within an algebraic function, determine the rate of change then use integration to find the area
under the graph to obtain the magnitude of the change between two points. Analyse the maxima
and minima of a higher order function and justify, using further differentiation,how we can be
sure that these are not saddle points.
*Please access HN Global for additional resources support and reading for this unit. For furtherguidance and
support on report writing please refer to the Study Skills Unit on HN Global www.highernationals.com
Learning Outcomes and Assessment Criteria
Pass
Merit
Distinction
LO1 Use applied number theory in practical computingscenarios
P1 Calculate the greatest
common divisor and least
common multiple of a given
pair of numbers.
P2 Use relevant theory to
sum arithmetic and
geometric progressions.
M1 Identify multiplicative
inverses in modular arithmetic. D1 Produce a detailed written
explanation of the importance
of prime numbers within the
field of computing.
LO2 Analyse events using probability theory and probability
distributions
P3 Deduce the conditional
probability of different
events occurring within
independent trials.
P4 Identify the expectation ofan
event occurring from a discrete,
random variable.
M2 Calculate probabilities
within both binomially
distributed and normally
distributed random
variables.
D2 Evaluate probability
theory to an example
involving hashing and load
balancing.
LO3 Determine solutions of graphical examples using
geometry and vector methods
P5 Identify simple shapes using
co-ordinate geometry.
P6 Determine shape
parameters using appropriate
vector methods.
M3 Evaluate the co-ordinate
D3 Construct the scaling of
system used in programming a
simple shapes that are
simple output device.
described by vector coordinates.
LO4 Evaluate problems concerning differential and integral
calculus
P7 Determine the rate of
change within an algebraic
function.
P8 Use integral calculus to
solve practical problems
involving area.
M4 Analyse maxima and
minima of increasing and
decreasing functions using
higher order derivatives.
D4 Justify, by further
differentiation, that a value isa
minimum.