CALCULATIONS in MathML
Proofs in Algebra, Geometry, Logic, and Trigonometry
Luqman Malik
token
WRT
CONTENTS
PART I.
ALGEBRA
Chapter 1.
Numbers
1.
The integers
2.
Rules for addition
3.
Rules for multiplication
4.
Even and odd integers | divisibility
5.
Rational numbers
6.
Multiplicative inverses
Chapter 2.
Linear Equations
1.
Equations in two unknowns
2.
Equations in three unknowns
Chapter 3.
Real Numbers
1.
Addition and multiplication
2.
Real numbers: positivity
3.
Powers and roots
4.
Inequalitites
Chapter 4.
Quadratic Equations
Interlude
on Logic and Mathematical Expressions
1.
On reading books
2.
Logic
3.
Sets and elements
4.
Notation
PART II.
PLANE GEOMETRY
Chapter 5.
Distance and Angles
1.
Distance
2.
Angles
3.
The Pythagorean Theorem
Chapter 6.
Isometries
1.
Some standard mappings of the plane
2.
Isometries
3.
Composition of isometries
4.
Inverse of isometries
5.
Characterization of isometries
6.
Congruences
Chapter 7.
Area and applications
1.
Area of a disc of radius
r
2.
Circumference of a circle of radius
r
PART III.
COORDINATE GEOMETRY
Chapter 8.
Coordinates and Geometry
1.
Coordinate systems
2.
Distance between points
3.
Equation of a circle
4.
Rational points on a circle
Chapter 9.
Operations on points
1.
Dilations and reflections
2.
Addition, Subtraction, and the parallelogram law
Chapter 10.
Segments, Rays, and Lines
1.
Segments
2.
Rays
3.
Lines
4.
Ordinary equation for a line
Chapter 11.
Trigonometry
1.
Radian measure
2.
Sine and cosine
3.
The graphs
4.
The tangent
5.
Addition formulas
6.
Rotations
Chapter 12.
Some Analytic Geometry
1.
The straight line again
2.
The parabola
3.
The ellipse
4.
The hyperbolo
5.
Rotation of hyperbolos
6.
Rotations
PART IV.
MISCELLANEOUS
Chapter 13.
Functions
1.
Definition of a function
2.
Polynomial functions
3.
Graphs of function
4.
Exponential function
5.
Logorithms
Chapter 14.
Mappings
1.
Definition
2.
Formalism of mappings
3.
Permutations
Chapter 15.
Complex Numbers
1.
The complex plane
2.
Polar form
Chapter 16.
Induction and Summations
1.
Induction
2.
Summations
3.
Geometric Series
Chapter 17.
Determinants
1.
Matrices
2.
Determinants of order 2
3.
Properties of 2×2 determinants
4.
Determinants of order 3
5.
Properties of order 3×3 determinants
6.
Cramer's Rule
Glossary
Figures
Π-Index
ſ-Index
Computations in MathML
▸
▾
▬
▬
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
▸
●
●
Calculations in MathML
PROLOGUE
FOUNDATIONS
Basic Properties of Numbers
Numbers of Various Sorts
Functions
Graphs
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
A1
01
02
03
04
05
06
07
A2
01
02
03
A3
01
02
03
04
05
06
07
08
09
10
Limits
Continuous Functions
Three Hard Theorems
Least Upper Bounds
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
01
02
03
04
05
06
07
08
09
10
11
12
13
14
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
01
02
03
04
05
06
07
08
09
10
11
12
13
DERIVATIVES & INTEGRALS
Derivatives
Differentiation
Significance of the Derivative
Inverse Functions
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Integrals
The Fundamental Theorem of Calculus
The Trigonometric Functions
π
is Irrational
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
01
02
03
04
05
06
07
08
09
10
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
INFINITE SEQUENCES & INFINITE SERIES
Planetary Motions
The Logarithm and Exponential Functions
Integration in Elementary Terms
Approximation by Polynomial Functions
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
e
is Transcendental
Infinite Sequences
Infinite Series
Uniform Convergence and Power Series
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
EPILOGUE
Complex Numbers
Complex Functions
Complex Power Series
Fields
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
01
02
03
04
05
06
07
08
09
10
11
12
13
14
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
Construction of The Real Numbers
Uniqueness of the Real Numbers
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
01
02
03
04
05
06
07
08
09
10
11
12
13
14
●
●