Summary

(By Chapter)


1. Simple functions
Displaying numbers neatly
Right-justified numbers
INT, the integral part of a number
ABS, the absolute value of a number
Rounding off numbers
Rounding up and down
Rounding off a number to D decimal places
Bank balances
Overdrawn bank balances
SGN, the sign or signum function
Displaying bank balances colourfully

2. Trigonometry
Scale drawings
Estimating heights and distances
Right-angled triangles
Trigonometric functions, TAN, SIN and COS
Hypotenuse, opposite side, adjacent side
Radian
PI
Degrees to radians, radians to degrees
Finding lengths of a right-angled triangle
Inverse functions
Arc tangent, ATN
Arc sine, ASN
Arc cosine, ACS
Pytharogas' theorem
Non right-angled triangles
Law of cosines
Law of sines
Finding angles and/or sides of a triangle
Refraction
Angle of incidence, angle of refraction
Snell's law
Refractive index
Reflection
Critical angle

3. Earth trigonometry
The Earth
Straight lines on the Earth
Great circles
Lines of longitude
Greenwich, England
Lines of latitude
Calculating the distance between two points on the Earth

4. Powers
Squares of numbers
Powers of numbers
Properties of powers
SQR, square root
Imaginary numbers
Complex numbers
Complex numbers on the BBC and Electron micros
Quadratic equations
Solving quadratic equations
Roots, finding roots
Formula for the roots of a quadratic equation
Discriminant
Solving quadratic equations on your computer
Solving other equations
Polynomial equation
Degree of a polynomial
Roots of polynomials
Newton's method
Derivative of a polynomial
Finding roots via Newton's method
EXP, the exponential function
E, EXP(1)
Factorial
Properties of the exponential function
Formula for exponential function
Logarithmic function
LN, the natural logarithmic function
Properties of the logarithmic function
Finding roots of other functions

5. Sequences
Sequences
Terms of a sequence
Generating sequences
Arithmetic sequence, arithmetic progression
Common difference
Generating arithmetic sequences
Which would you prefer?
Geometric sequence, geometric progression
Common ratio
Generating geometric sequences
Interest, compound interest
Daily interest
Double or quit gambling
Fibonacci sequences
Generating Fibonacci sequences

6. Number bases
Decimal system
Digits
Decimal representation
Base
Coefficients of a number N to a base B
Binary number system
Hexadecimal numbers
Converting numbers from one base to another
Numbers on computers
PEEKing at numbers
Binary form of numbers between 0 and 1
Displaying binary from of numbers between 0 and 1
Floating points
Binary exponent
Binary mantissa

7. Days and weeks
Days of the week
Zeller's congruence
Finding the day of the week for any given date
Displaying a monthly calendar for any month, any year
Date management
Pseudo-Julian date
Listing dates a specified number of days apart

8. Greatest common divisor
Common divisor, common factor
Greatest common divisor, highest common factor
Euclidean algorithm
Calculating the greatest common divisor
Least common multiple
Calculating the least common multiple

9. Primes
Prime number
Composite number
There are infinitely many prime numbers
Sieve of Erastosthenes
Prime testing
Finding factors
Large primes
Mersenne numbers, Mersenne primes
Largest known prime
Probabilistic primality testing
Fermat's little theorem
Pseudoprime to a base
Most pseudoprimes are genuine primes

10. Odds and ends
Pythagorean triplets
Primitive Pythagorean triplets
Multi-precision powers
Calculating products of large numbers accurately on your computer
Calculating arbitrary large powers accurately

11. Matrices
Matrices, rectangular arrays of numbers
M by N matrix
Square matrix
Adding matrices
Why add matrices
Matrix multiplication
Why multiply matrices?
Zero matrix
Identity matrix
Inverse of a matrix, reciprocal of a matrix
Calculating the inverse of a matrix
Simultaneous matrices
Solving simultaneous matrices

12. Codes
Cryptography
Ciphers
Substitution codes
Sample substitution code program
Matrix codes
Using matrices to cipher messages
Sample matrix code program
Public-key codes
Prime numbers and secure codes

13. Random!
Heads and tails
Tossing coins
Random numbers
Simulating coin spinning on a computer
Of dice and men
Die rolling
Probability
Simulating die rolling
Simulating two dice rolling
Playing cards
Simulating card picking
Shuffling a pack of cards randomly
Non-equally likely events
Bucket with 100 coloured buttons
Simulating button picking from a bucket

14. Meaningful data
Entering numerical data into a computer
Mean, average
Calculating the mean
Maximum and minimum
Spread, range
Calculating the max, min and spread
Standard deviation
Variance
Calculating the standard deviation
Confidence intervals
Normal distribution
Calculating confidence intervals for a population
Calculating confidence intervals for the mean
Student's t distribution


Other titles from Sunshine

SPECTRUM BOOKS      


Spectrum Adventures
A guide to playing and writing adventures
Tony Bridge & Roy Carnell   £5.95
ISBN 0 946408 07 6
ZX Spectrum Astronomy
Maurice Gavin   £6.95
ISBN 0 946408 24 8
Spectrum Machine Code Applications
David Laine   £6.95
ISBN 0 946408 17 3
The Working Spectrum
David Lawrence   £5.95
ISBN 0 946408 00 9
Master your ZX Microdrive
Andrew Pennell   £6.95
ISBN 0 946408 19 X

COMMODORE 64 BOOKS      


Graphic Art for the Commodore 64
Boris Allan   £5.95
ISBN 0 946408 15 7
DIY Robotics and Sensors on the Commodore Computer
John Billingsley   £6.95
ISBN 0 946408 30 0
Artificial Intelligence on the Commodore 64
Keith & Stephen Brain   £6.95
ISBN 0 946408 29 7
Commodore 64 Adventures
Mike Grace   £5.95
ISBN 0 946408 11 4
Business Applications for the Commodore 64
James Hall   £5.95
ISBN 0 946408 12 2
Mathematics on the Commodore 64
Czes Kosniowski   £5.95
ISBN 0 946408 14 9
Advanced Programming Techniques on the Commodore 64
David Lawrence   £5.95
ISBN 0 946408 23 8
The Working Commodore 64
David Lawrence   £5.95
ISBN 0 946408 02 5
Commodore 64 Machine Code Master
David Lawrence & Mark England   £6.95
ISBN 0 946408 05 X

ELECTRON BOOKS      


Graphic Art for the Electron Computer
Boris Allan   £5.95
ISBN 0 946408 20 3
Programming for Education on the Electron Computer
John Scriven & Patrick Hall   £5.95
ISBN 0 946408 21 1

BBC COMPUTER BOOKS      


Function Forth for the BBC Computer
Boris Allan   £5.95
ISBN 0 946408 04 1
Graphic Art for the BBC Computer
Boris Allan   £5.95
ISBN 0 946408 08 4
DIY Robotics and Sensors for the BBC Computer
John Billingsley   £6.95
ISBN 0 946408 13 0
Programming for Education on the BBC Computer
John Scriven & Patric Hall   £5.95
ISBN 0 946408 10 6
Making Music on the BBC Computer
Ian Waugh   £5.95
ISBN 0 946408 26 2

DRAGON BOOKS      


Advanced Sound & Graphics for the Dragon
Keith & Steven Brain   £5.95
ISBN 0 946408 06 8
Dragon 32 Games Master
Keith & Steven Brain   £5.95
ISBN 0 946408 03 3
The Working Dragon
David Lawrence   £5.95
ISBN 0 946408 01 7
The Dragon Trainer
A handbook for beginners
Brian Lloyd   £5.95
ISBN 0 946408 09 2

ATARI BOOKS      


Atari Adventures
Tony Bridge   £5.95
ISBN 0 946408 18 1
Writing Strategy Games on your Atari Computer
John White   £5.95
ISBN 0 946408 22 X


Sunshine also publishes

POPULAR COMPUTING WEEKLY

The first weekly magazine for home computer users. Each copy contains Top 10 charts of the best-selling software and books and up-to-the-minute details of the latest games. Other features in the magazine include regular hardware and software reviews, programming hints, computer swap, adventure corner and pages of listings for the Spectrum, Dragon, BBC, VIC 20 and 64, ZX 81 and other popular micros. Only 35p a week, a year's subscription costs £19.95 (£9.98 for six months) in the UK and £37.40 (£18.70 for six months) overseas.

DRAGON USER

The monthly magazine for all users of Dragon microcomputers. Each issue contains reviews of software and peripherals, programming advice for beginners and advanced users, program listings, a technical advisory service and all the latest news related to the Dragon. A year's subscription (12 issues) costs £10 in the UK and £16 overseas.

MICRO ADVENTURER

The monthly magazine for everyone interested in Adventure games, war gaming and simulation/role-playing games. Includes reviews of all the latest software, lists of all the software available and programming advice. A year's subscription (12 issues) costs £10 in the UK and £16 overseas.

COMMODORE HORIZONS

The monthly magazine for all users of Commodore computers. Each issue contains reviews of software and peripherals, programming advice for beginners and advanced users, program listings, a technical advisory service and all the latest news. A year's subscription costs £10 in the UK and £16 overseas.

For further information contact:
Sunshine
12-13 Little Newport Street
London WC2R 3LD
01-437 4343