mathematics for software

HND Assignment Brief
Programme title BTEC HND in Computing and Systems Development (CSD)
Unit number and title Unit 23 Mathematics for Software Development
Assignment number &
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Student name and No
Assessor (s) John Dwyer – Musie Beyene
Issue date 07/10/2013 Deadline(s)
Written
Work:
13-18/01/2014
Resubmission Y Deadline TBA
Late submission:
Work submitted after the deadline, and within 2 weeks of the
deadline, will be capped at a pass grade unless extenuating
circumstances apply- see programme handbook for further
information. Work submitted later than two weeks after the deadline
will not be accepted.
Feedback Feedback will be available within 3 to 4 weeks of the submission
date.
Evidence checklist
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hand in the right
work
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1. All Tasks answers provided in required
format, word processed, cited with accurate
sources where required.
2. All supportive materials supplied in Appendix,
suitably titled and cross referenced to body of
text.
3. Turnitin report has been attached.
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ICON College of Technology and Management
BTEC HND in Computing and Systems Development
(CSD)
Unit 23: Mathematics for Software Development (L4)
Session: September 2013
Coursework
No formal word limit
This Unit will be assessed by Assignments and Time Constraint Assessment
(TCA).
You are strongly recommended to read “Preparation guidelines of the
Coursework Document (section 3)” before answering your assignment.
LO1: Understand core mathematical skills for software engineers
A. BASIC ALGEBRA & GEOMETRY EXERCISES
A1. Solve the following linear and quadratic equations:
(i) (11x – 5) = 5
(ii) 2(3 – 5x) = 15
(iii) x2 − 3x + 2 = 0
(iv) 6x2 − 16x + 10 = 0
A2. Solve the following sets of simultaneous equations by (a) algebraic method (b) graphical
method.
(i) y = 3x + 1; y = −3x + 1
(ii) y = 3x + 1; y = −5x + 17
(iii) −4y = 2x − 4; 3y = x + 7
(iv) 7y = 8x + 6; 6y = −3x − 13
A3. Find the areas of the following shapes to three significant figures:
(i) a circle with diameter 30 metres (ii) a triangle with sides 20, 21 and 29
inches
A4. Create a spreadsheet to illustrate the use of at least TEN functions contained in the
“Mathematical and trigonometry functions” section of Appendix E shown on page 93. You
will need to develop your own table of decimal numbers and angle values.
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B. ARRAYS, MATRICES & VECTORS EXERCISES
B1.
The (x,y) co−ordinates of the defining points in the above shape are (0,0), (1,0), (1,1) and
(2,1). Sketch the co−ordinates of the new shape generated by the following transformation
matrix equations:
(i) =
(ii) =
In each case, briefly summarize the resulting effect, e.g. “translation to the right of one
unit”.
B2. A part of the code for a “games” computer program which relates to arrays is shown in
the figure below:
char [] coinfaces = { 'H','T'};
char [] diespots = { '1','2','3','4','5','6'};
(i) Write down the dimensions of the arrays coinfaces and diespots,
(ii) Assuming that a standard pack of playing cards comprises four suits,
each with thirteen ranks, write similar new lines of code for the arrays
suits and ranks.
–3 –2 –1 1 2 3
–1
1
2
–2
x
y
(1,1)
(0,0) (1,0)
(2,1)
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B3. Given that the magic number corresponding to a 4−by−4 magic square is 34 and
corresponding to a 5−by−5 magic square is 65, write down and complete the entries for
following magic squares:
15 14 4 24 1 8 15
12 6 7 23 5 7 14 16
8 10 4 6 13 20
13 10 12 19
11 18
B4. In a UK company, setting up an in−house IT dept costs an initial set−up cost of £50K plus
ongoing annual costs of £75K per year while sub−contracting out IT costs a regular fixed
annual cost of £85K. Use an augmented matrix method to calculate the number of years it will
take before the cost of each is the same.
B5. Solve the following Sudoku puzzle:
6 5 7 2 9 3 1 8 4
8 2 4 6 3
3 9 8 5 7
7 8 1 4 6
5 8 6 7 3 2 4 9 1
2 9 6 5 8
1 8 5 6 2
4 6 2 1 9
9 3 2 1 7 6 8 4 5
B6. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 ARRAYS, MATRICES & VECTORS
Note that the primary objective in each case is to appreciate how the mathematics is carried out in a relatively
simple way, not to try to present very complex code.
For instance the following Java code would produce the Boolean (logical) output shown:
public class Test {
public static void main(String args[]) {
boolean a = true;
boolean b = false;
System.out.println("a && b = " + (a&&b));
System.out.println("a || b = " + (a||b) );
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System.out.println("!(a && b) = " + !(a && b));
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}
Output:
a && b = false
a || b = true
!(a && b) = true
Reference:
http://www.tutorialspoint.com/java/java_logical_operators_examples.htm
LO2: Understand the application of algebraic concepts
C. COMBINATORICS & FACTORIALS
C1. If a card security PIN system comprising the decimal digits 0 through 9is extended from
four to six digits, how many different variations are possible, assuming that:−
(i) it is allowed to repeat digits,
(ii) it is not allowed to repeat digits.
C2. The following version of Pascal’s triangle contains two errors. Find the errors.
C3. The number of permutations of n characters when k characters are the same is given by:
n!
k!
So for instance the number of permutations of the characters “EGG” is 3!/2! = 3 (namely,
“EGG”,”GEG”, GGE”).
Calculate the number of character permutations of:
(i) “DWYER”,
(ii) “JOADAT”,
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(iii) “ICONCOLLEGE”
(iv) “JOSEMOURINHO”.
C4. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 COMBINATORICS & FACTORIALS
Note that the primary objective in each case is to appreciate how the mathematics is
carried out in a relatively simple way, not to try to present very complex code.
LO3: Be able to apply the fundamentals of formal methods
D. PROBABILITY, SETS & RELIABILTY
D1. Suppose that two sets are A and B, defined by
A = { r, o, m, a, n, i, a }
B = { n, i, g, e, r, i, a }
Identify the following statements as true or false:
(i) a ∈ A,
(ii) b ∈ B,
(iii) g ∉ B,
(iv) u ∉ A,
(v) i ∈ A⋂B,
(vi) |A| = |B|,
(vii) { i, r, a, n} ⊂ A,
(viii) |A⋃B| = 14,
D2. Suppose we have a universal set {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19} and
consider two sets P and O defined as follows:
P = “the first eight prime numbers”
O = “the first ten odd numbers”
Represent all of the elements in a Venn diagram and identify the elements in P⋂O, P⋃O
and PΔO.
D3. For all of the following sets defined in set−theoretic notation, list out all of the elements:
S1 = {x: x = 2n, where 1 ≤ n ≤ 6}
S2 = {x: x = 3n, where 1 ≤ n ≤ 5}
S3 = {x: x = 4n, where 1 ≤ n ≤ 4}
S4 = {x: x = 4n, where 1 < n < 3}
S5 = {x: x = n2, where 1 ≤ n ≤ 4 }
S6 = {x: x = n3, where 1 ≤ n < 4 }
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D4.
The sample space above represents throwing two dice where each ordered pair gives the
number thrown on the first and second die, respectively. So, for instance, (1,5) represents
throwing “1” on the first die and “5” on the second. By choosing a suitable reduced sample
space in each case, calculate the following conditional probabilities:
(i) Throwing an even total number, given a condition that the second die shows “6”,
(ii) Throwing an odd total number, given a condition that the first die shows “1”,
(iii) Throwing a “1” on the first die, given a condition that the total on both is seven.
D5. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 PROBABILITY, SETS & RELIABILTY
Note that the primary objective in each case is to appreciate how the mathematics is carried out in a relatively
simple way, not to try to present very complex code.
E. RELATIONS & FUNCTIONS
E1. Suppose that three siblings in a family are Ahmed, Bernadette and Christina. Represent
the following relations in a relation diagram:
a) Rs, “is the sister of”,
b) Rb, “is the brother of”,
c) Rs', “is not the sister of”,
d) Rb', “is not the brother of”
E2. For the following relations, sketch a suitable co−ordinate diagram and mapping diagram,
and identify those which are also functions:
a) “half” y = x / 2; domain { 2, 4, 6 }; range { 1, 2, 3 },
b) “square root” y = ; domain { 0, 1, 4 }; range { −2,−1, 0, +1, +2 },
c) “square” y = ; domain { −2,−1, 0, +1, +2 }, range { 0, 1, 4 }.
d) “absolute” y = |x|; domain { −2,−1, 0, +1, +2 }, range { 0, 1, 2 }.
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E3. For a database comprising two tables of information (shown below), list by last name the
individuals satisfying the conditions (a) – (d).
Last_Name First_Name City Age Salary
Abrahams John 2 31 €18,000
Diaz Elena 1 29 €37,000
Brown Steven 2 43 €23,000
Pacilis Dimitris 3 19 €15,000
Larsson Tomas 4 23 €20,000
City City_Name
1 Madrid
2 London
3 Athens
4 Stockholm
a) (Age > 20) AND (Salary > €21,000),
b) (Age >20) OR (Salary > €21,000),
c) (Age > 30) AND (City = 2)AND (Salary > €20,000),
d) (Age < 30) OR (City = 2) OR (Salary > €20,000).
E4. Create a spreadsheet to illustrate the use of at least THREE database functions
contained in the “Database Function” section of Appendix E shown on page 90. You
will need to develop your own simple database containing some number entries.
E5. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 RELATIONS & FUNCTIONS
Note that the primary objective in each case is to appreciate how the mathematics is
carried out in a relatively simple way, not to try to present very complex code.
F. BOOLEAN ALGEBRA & PROPOSITIONAL LOGIC
F1. For the circuit shown below, construct a truth table for each intermediate function. Hence,
find the output function X.
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F2. For the PLA shown in Application 1 of the unit text (page 43), sketch circuits for Outputs
O1, O2 and O3 similar to the one shown for Output O4.
F3. What would be the printed output of the following code.
boolean a = true;
boolean b = true;
boolean c = a == b;
System.out.println("c = " + c);
F4. Create a spreadsheet to illustrate the use of all SIX logical functions contained in the
“Logical functions” section of Appendix E shown on page 89. You will need to develop
your own simple table of logical values.
F5. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 BOOLEAN ALGEBRA & PROPOSITIONAL LOGIC
Note that the primary objective in each case is to appreciate how the mathematics is
carried out in a relatively simple way, not to try to present very complex code.
LO4: Be able to apply statistical techniques to analyse data
G. STATISTICAL TECHNIQUES & DISTRIBUTIONS AND MISCELLANEOUS EXERCISES
G1. Consider the following grouped data relating to the number of syntax errors contained in
computer programs written by the thirty students. Represent the data in a histogram and
in a pie chart.
No. of Errors ≤1 2 3 4 5 6 7 8 ≥9
Frequency 0 2 3 10 9 3 2 1 0
Find the following:
Output X
A1
A2
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(i) the probability of choosing a program at random from this sample that has ≤ 3
errors
(ii) the probability of choosing a program at random from this sample that has ≤ 1
errors
(iii) the probability of choosing a program that has ≤ 1 errors, assuming a normal
distribution
G2. Carry out a statistical experiment in the classroom to select a random sample of ten
members of your class and obtain
a) The mean height of sample
b) The standard deviation in height of the sample
c) The probability of selecting a member of your sample with height greater than 6’6”
d) Assuming a normal distribution with the same mean and standard deviation as your
sample, the probability of selecting a member of your sample with height greater than
6’6”
Represent your sample distribution and normal distribution in the form of a histogram
and normal curve, respectively.
G3. Create a spreadsheet to illustrate the use of at least FIVE statistical functions contained
in the “Statistical functions” section of Appendix E shown on page 94 of text book. You
will need to develop your own simple database containing some number entries.
G4. There are several popular languages for software development, including Java, C#, and
Prolog. Selecting any language of your choice, present code fragments to highlight the
following mathematical categories investigated in the unit:
 STATISTICAL TECHNIQUES & DISTRIBUTIONS
Note that the primary objective in each case is to appreciate how the mathematics is
carried out in a relatively simple way, not to try to present very complex code.
Relevant information
1. General grading criteria of this coursework
Outcomes Assessment criteria for pass Questions reflecting
the outcome
LO1: Understand
core
mathematical
skills for software
engineers
1.1 design a programming solution to a given algebraic
problem
1.2 design a programming solution to a given geometric
problem
1.3 implement code that presents a range of vectors
A1 – A4
B1 – B6
B1 – B6
LO2: Understand
the application of
algebraic
concepts
2.1 explain how relations link to technologies used in
programming
2.2 design a programming solution to solve a matrix
manipulation problem
C1 – C4; E1 – E5
B1 – B5
LO3: Be able to
apply the
3.1 discuss the application of set theory in computing
3.2 design a programming solution to a given propositional
D1 – D5
F1 – F5
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fundamentals of
formal methods
calculus problem
LO4: Be able to
apply statistical
techniques to
analyse data
4.1 design a programming solution to solve a given
statistical analysis technique
G1 – G3
2. Grading Criteria for Merit and Distinction of this coursework
Merit (M1, M2, M3) Distinction (D1, D2, D3)
Descriptors Indicative characteristics Descriptors Indicative characteristics
M1 - Identify and
apply strategies to
find appropriate
solution
 Pass requirements achieved
 complex problems with more
than one variable have been
explored
D1 - Use critical
reflection to
evaluate own work
and justify valid
conclusions
 Pass and Merit
requirements achieved
 The validity of results has
been evaluated using
defined criteria
M2 - Select/design
and apply
appropriate
methods/techniques
 Relevant theories and
techniques have been applied
 A range of methods and
techniques have been applied
 A range of sources of
information has been used
 Appropriate learning
methods/techniques have
been applied
D2 - Take
responsibility for
managing and
organising activities
 Autonomy/independence
has been demonstrated
M3 - Present and
communicate
appropriate findings
 A range of methods of
presentation has been used
and technical language have
been accurately used
D3 - Demonstrate
convergent/lateral/c
reative thinking
 Ideas have been generated
and decisions taken
 Problems have been
solved
3. Preparation guidelines of the Coursework Document
a. All coursework must be word processed.
b. Document margins must not be more than 2.54 cm (1 inch) or less than 1.9cm (3/4 inch).
c. Font size must be within the range of 10 point to 14 point including the headings and body text.
d. Standard and commonly used type face such as Times new Roman or Arial etc should be used.
e. All figures, graphs and tables must be numbered.
f. Material taken from external sources must be properly refereed and cited within the text using
Harvard standard
g. Word limit must be strictly followed.
4. Plagiarism and Collusion
Any act of plagiarism or collusion will be seriously dealt with according to the regulations. In this
context the definition and scope of plagiarism and collusion are presented below: Plagiarism is
presenting somebody else’s work as your own. It includes copying information directly from the Web or
books without referencing the material; submitting joint coursework as an individual effort.
Collusion is copying another student’s coursework; stealing coursework from another student and
submitting it as your own work.
Suspected plagiarism or collusion will be investigated and if found to have occurred will be dealt with
according to the college procedure.(For details on Plagiarism & Collusion please see the student
hand book)
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5. Submission
a. Initial submission of coursework to the tutors is compulsory in each unit of the course.
b. Students must attach their initial feedback copy with their final submission of the coursework.
The exam office will not receive any final coursework without initial feedback.
c. Student must check their assignments on Moodle site with plagiarism software TurnItIn and
obtain a certificate.
d. All Final coursework must be submitted to the assigned person (not to the Tutor) and a receipt
must be obtained. Under no circumstances other College staffs accepts them.
e. The copy of the coursework submitted will not be returned to you after marking.
f. The student must attach a copy of the question in between the cover page and the answer.
6. Good practice
a. Make backup of your work in different media (hard disk, CD, memory stick etc) to avoid distress for
loss or damage of your original copy.
b. Make an extra hardcopy of your work submitted for your own reference or later use
7. Extension and Late Submission
a. If you need an extension for a valid reason, you must request one using a coursework extension
request form available from the college. Please note that the lecturers do not have the authority to
extend the coursework deadlines and therefore do not ask them to award a coursework extension.
The completed form must be accompanied by evidence such as a medical certificate in the event
of you being sick.
b. Late submission will be accepted and marked according to the college procedure. It is noted that
late submission may result in lower grade or rejection.
8. Submission deadlines
Initial Submission 9 – 14 Dec. 2013
Feedback given 16 – 21 Dec. 2013
Final Submission 13 – 18 Jan. 2014
Submit to: Mr Mahbubur Rahman
Examination Officer
Room ICTM 207
Unit 21, 1-13 Adler Street
E1 1EG
The assignment exercises cover topics drawn from the Unit Text “Mathematics for Software
Development” (Dwyer & Joadat, 2013).
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