Mathematics for Software Development Essay Example

  • Category:
    Logic & Programming
  • Document type:
    Coursework
  • Level:
    Undergraduate
  • Page:
    2
  • Words:
    1229

LO1: understand core mathematical skills form software engineers

A1. Solve the following linear and quadratic equations:

  1. 2(3-5x)=15

  2. Mathematics for Software Development

i). 2(3 – 5x) = 15

6-10x =15

10x=15-6

Mathematics for Software Development 1
X=0.9 or

+ x -20 = 0 2ii). x

Mathematics for Software Development 2
Using

Mathematics for Software Development 3Mathematics for Software Development 4=

Mathematics for Software Development 5

Mathematics for Software Development 6

.algebraic methodA2. Solve the following sets of simultaneous equations by (a) algebraic method and (b)

(a) Algebraic method

i). y=2x; y=-2x+1

=-2x+1Thus 2x

4x =1, x=1/4, y=1/2

ii). y = 5x + 1; y =−5x + 1

5x + 1 =−5x + 1Thus

iii). −6y = 3x − 4; 2y = x + 5

x=2y-5Thus

−6y = 3(2y-5) – 4

−6y = 6y-15 − 4

Mathematics for Software Development 712y = 19; y=19/12 or 1

x=-1.833

(b) Graphical method.

y=2x; y=-2x+1

Mathematics for Software Development 8

y = 5x + 1; y =−5x + 1

Mathematics for Software Development 9

6y = 3x − 4; 2y = x + 5 −

Mathematics for Software Development 10

Y=1.58, x=-1.833

A3. Find the volume of the following shapes to three significant figures by showing your work step by: [P1.2]

  1. A cube with a length of one side 27 metres

Volume = L x W x H

3Volume = 27 x 27 x 27 = 19,683m

  1. A sphere with radius 20 inches

,3Volume = (4/3)*pi*R

3 inches = 33,510.323Volume = (4/3)*pi*20

(9:12:15) is a right-angled triangle. Mathematics for Software Development 11
A4. Using Pythagoras theorem, proof that

2= 152+1229

81+144 =225

Mathematics for Software Development 12
(i). calculate sine, cosine and tangent for each angles of

Mathematics for Software Development 13

Mathematics for Software Development 14

Mathematics for Software Development 15

Sine Function:

) = Opposite / Hypotenuseθsin(

Sin(B)= 15/15 =1.00

Sin(B)= 9/15=0.6

Sin(B)= 12/15 =0.8

Cosine Function:

) = Adjacent / Hypotenuseθcos(

Cosine(B)= 0/15 =0.00

Cosine(C)= 12/15=0.8

Cosine(A) = 9/15 =0.6

Tangent Function:

) = Opposite / Adjacentθtan(

Tan(B)= 15/9 =1.333

Tan(A) =12/9 =1.333

Tan(B) = 9/12 =0.75

is a right angled triangle.Mathematics for Software Development 16
(ii). Using an appropriate Excel function, demonstrate on a spreadsheet that

A5. Two robots, Alice and Bob are pulling a box as shown on the figure: [P1.3, M1]

  1. Calculate vectors c= a+b.

Mathematics for Software Development 17

  1. Calculate magnitude vector c.

Mathematics for Software Development 18= 22.8

Write a pseudo code for calculating magnitude of vector c

);14,18(PVectornew=velocity

);-6,5(PVectornew=vector Alice

vector bob(13,20);

void setup() {

;velocityPVector

;positionPVector

LO2: understand the application of Algebraic concepts

B1. A certain British company has three departments. Following sets are showing departments, surnames and annual salaries of employees of this company:

A= (Martin, Marriott, Boast, Preston, Kans

B = (24k, 25k, 26k, 27k, 30k)

C = (production, sales, finance)

Mr Martin and Mrs Marriott are working at production department, Mrs Boast and Mrs Preston working at sales departments and Mr Kans works at Finance department.

  1. B)Mathematics for Software Development 19Find the Cartesian product of set A and set B. (R=A

    • R(B)Í B, then R(A) ÍIf A

    • R(B)È B) = R(A) ÈR(A

    • R(B)Ç R(A) Í B) ÇR(A

  1. Mathematics for Software Development 20Find the Natural join of R and C. (R

Mathematics for Software Development 21=

  1. Fill in the below table by using provided information:

Employee name

Department

production

Marriott

production

B2. A small ICT firm, has three branches in

  1. Redbridge,

  2. Enfield and

  3. Five technicians with following details are working at this company;

Ali (Location; Barnet, age: 25, salary€21,000).

Steve (Location, Redbridge, age: 45, salary: 23,000).

Mike (Location: Barnet, age: 50, Salary 19,000)

Linda (location; Barnet, age 55, salary 24,000

Carol (location; Redbridge, age 43, salary 27,000

  1. Draw required number of tables and fit in the above information there.

  2. List individual satisfying the conditions below.

  1. (Age<46) AND (salary> € 23,000)- Carol

  2. (Age>26) OR (salary<€24,000)- Mike and Steve

  3. (Age<53) AND (salary>29) OR (location=1)- none

  4. (Age>25) XOR (salary>30) OR (locations=2)- none

B3. Create a magic square by identifying value of p, q, r, s, t, u, x, y, z in matrix A. [P2.2]

Mathematics for Software Development 22
A=

Mathematics for Software Development 23
A=

Mathematics for Software Development 24
A=

{Show your work step by step}

B4. Show that if

Mathematics for Software Development 25P=

Mathematics for Software Development 26
Q=

Then p is the inverse of Q.

Mathematics for Software Development 27Mathematics for Software Development 29
= Mathematics for Software Development 28
=

or

, we can follow these steps:Mathematics for Software Development 30 To find the inverse of the matrix

Step 1) Find the determinant

Mathematics for Software Development 33 . So this means that Mathematics for Software Development 32 is Mathematics for Software Development 31 of determinant The

Step 2) Swap the values

Mathematics for Software Development 35 to get Mathematics for Software Development 34 Now switch the highlighted values

Step 3) Change the sign

Mathematics for Software Development 37 to get Mathematics for Software Development 36 Now change the sign of the highlighted values

Step 4) Multiply by the inverse of the determinant

Mathematics for Software Development 41 to get Mathematics for Software Development 40 Plug in

Mathematics for Software Development 39 to get Mathematics for Software Development 38 Multiply by

Step 5) Multiply Mathematics for Software Development 42 by every element in the matrix (simplify and reduce if possible)

Mathematics for Software Development 46 Reduce each element:
Mathematics for Software Development 45 Multiply to get
Mathematics for Software Development 44 by EVERY element to get Mathematics for Software Development 43Multiply

LO3: be able to apply the fundamentals of formal methods

C1. Suppose that two sets are A and B. defined by [P3.1]

A= (g, e, r, m, a , n, i)

B= {p, o, l, a, n, d}

Identify the following statements as true or false:

  1. — TrueMathematics for Software Development 47a

  2. — trueMathematics for Software Development 48
    b

  3. — FalseMathematics for Software Development 49d

  4. Mathematics for Software Development 50u

  5. Mathematics for Software Development 51
    a

  6. |A| =|B|- False

  7. Mathematics for Software Development 52
    (I, r, a, n)

  8. – False |AUB|= 8

C2, suppose we have universal set

21,22,23,24,25,26,27},15,16,17,18,19,20,{1,2,3,4,5,6,7,8,9, 10, 11,12,13,14

Two sets P and O defined as follows:

P= “all multiples of 3”

O= “the first ten even numbers”

O. [P3.1]Mathematics for Software Development 54, PUO and POMathematics for Software Development 53Represent all of the elements in a Venn diagram and identify the elements in P

Mathematics for Software Development 55

C3. For all of the following sets defined in a set-theoretic notation, list out all the elements: [P3.1, M3]

Mathematics for Software Development 56x is the element Mathematics for Software Development 571

Mathematics for Software Development 58 — x is the elementMathematics for Software Development 591

Mathematics for Software Development 60 x is the elementMathematics for Software Development 611

Mathematics for Software Development 62x is the elementMathematics for Software Development 631

C4. For the circuit shown below, construct a truth table for each intermediate function; hence, find the output function x. [P3.2]

0

0

0

0

0

0

0

0

0

0

0

0

0

0

C5. Suppose that a salesman has 4 differently-located customers. [P3.2]

  1. Find the number of differently ways that the salesman can leave home visit two different customers and are then return home.

Mathematics for Software Development 64= 12

  1. Write a pseudo code for calculating the answer for the previous section.

}; // class Tsp_map

return tour;

tour[i] = i;

for(int i = 0; i < size(); ++i) {

vector<int> travel(size());

vector<int> get_default_tour() const {

return home.size();

int size() const {

// # of customers

Point p(x, y);

void add(double x, double y) {

// add a customer at (x, y)

customer.push_back(p);

void add(const Point& p) {

// add a customer at point p

vector<Point> customers;

private:

class Tsp_map {

#include «Point.h»

LO4: be able to apply statistical techniques to analyze data

D1. A research in 157 households found that the number of children per household is

Children

0

Household

  1. Calculate the mean of frequency distribution for the above case.

Mean = 157/6 = 26.17

  1. What is the mode value of number of children’s per household?

The mode value is the number that occurs most in the data and in this case there is no mode.

D2. A company has ten sales territories with approximately the same number of sales people working in each territory. Last month the sales orders achieved were as follows:

For these sales calculate the following:

= 150Mathematics for Software Development 66
= Mathematics for Software Development 65Arithmetic mean =

Mode = 140

,140, 150,150,300140,140Median = 110 120,120, 130,

= 140Mathematics for Software Development 67
Median =

,140, 150,150,300140,140, 130, 120,120Lower quartile = 110

= 120Mathematics for Software Development 68
Lower quartile =

Upper quartile

,300150,150,140, 140,140110 120,120, 130,

= 150Mathematics for Software Development 69
Upper quartile =

Quartile deviation 1/2(Q_3 –Q_1) = ½(150-120) =15

Standard deviation

2(x-150)

0

0

0

0

= 54.37Mathematics for Software Development 71
= Mathematics for Software Development 70
Standard deviation =

= 30Mathematics for Software Development 73
= Mathematics for Software Development 72Mean deviation =

Show all the steps you took to complete your answer.

D3]cIdentify a topic in one of the following areas and conduct a research on it applications in software development. [P4.1

Boolean algebra

There are a number of appropriate sites relating to the use of Boolean algebra for analysing and designing logic gates,

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