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CM 1015 Computational Mathematics
Preface
How to Prove It
1
Number Bases, Conversion and Operations
1.1
Number Bases
1.2
Why different bases matter? (optional)
1.2.1
Comparison of Typical Use Cases
1.2.2
Why They’re Important
1.3
Number Conversion
1.3.1
Converting from Decimal to Other Number Base
1.3.2
Conversion Shortcuts with Binary Number
1.3.3
Non-integer Number Conversion
1.4
Operations with Binary Number
1.5
Negative Numbers in Binary (optional)
2
Series and Sequence
2.1
Little Gauss (optional)
2.2
Sequence
2.3
Series
2.4
Recursive Sequences
3
Modular Arithmetic
3.1
Congruence
3.2
Operations in Modular Arithmetics
3.3
Fermat’s Little Theorem (optional)
4
Introduction to Trigonometry
4.1
Angles
4.1.1
Units of Measurement
4.1.2
Type of Angles
4.2
Triangles
4.2.1
Special Triangles
4.2.2
Similar Triangles
4.2.3
Pythagoras’ Theorem
4.3
Trigonometric Relations
4.3.1
Basic Ratios (Right Triangles)
4.3.2
Law of Sines
4.3.3
Law of Cosines
4.3.4
Special Angles (Summary Table)
5
Functions and Graphs
5.1
Numbers and Intervals
5.1.1
Number Sets
5.1.2
Intervals on the Real Line
5.2
Functions
5.2.1
Introduction to functions
5.2.2
Type of Functions
5.2.3
Composite Functions
5.2.4
Inverse Functions
5.2.5
Properties of Function
5.3
Graph Sketching
5.4
Application of Functions
6
Kinematics
6.1
Introduction to Kinematics
6.2
Motion as a Function
6.3
Graphical Interpretation
6.4
Worked Examples
7
Trigonometric Functions
7.0.1
Pythagorean Identities
8
Exponential and Logarithmic Functions
9
Limit and Differentiation
10
Linear Algebra, Vector and Matrices
11
Combinatorics and Probability
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CM 1015 Computational Mathematics
Chapter 11
Combinatorics and Probability
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