Numerates
Course Content
Topic outline
General
Geometry Lesson 1
Geometry Lesson 1
In this lesson, we shall learn about the concept of area and how to use it to solve problems from AMC 8, MATHCOUNTS, and similar contests.
1. Area of a rectangle
2. Area of a circle
3. Areas of triangles having shared bases or shared heights.
4. Area of an equilateral triangle.
5. Area of a sector.
Geometry Lesson 4
Geometry Lesson 4
The focus of this lesson will be to study the concepts of tangents and secants of a circle. We shall give their definitions and also discuss some properties.
1. Tangents
2. Secants
3. A property of tangent lines.
- Opened: Monday, 7 March 2022, 12:00 AMDue: Monday, 14 March 2022, 12:00 AM
Geometry Lesson 5
Geometry Lesson 5
In this lesson, we shall discuss the premise of coordinate geometry and also see some properties of the basic geometric objects, such as points, lines, and circles.
1. The basic idea of coordinate geometry
2. Lines and circles
3. The section formula
4. The distance formula
5. Area of a triangle in terms of its vertices.
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Geometry Lesson 6
Geometry Lesson 6
We shall begin this lesson by introducing the concept of a transformation of a plane. We shall then define symmetries in terms of these transformations.
1. Transformations of the plane
2. Basic isometries
3. Types of symmetries.
- Opened: Saturday, 5 March 2022, 12:00 AMDue: Saturday, 12 March 2022, 12:00 AM
Algebra Lesson 1
Algebra Lesson 1
In this lesson, we shall discuss the concepts of ratios and percentages, which are fundamental to all of Mathematics.
1. Ratios.
2. Percentages.
Algebra Lesson 2
Algebra Lesson 2
Strictly speaking, the measures of central tendency and dispersion belong to the field of Statistics. They are used to get quantitative information about sets of data. In this lesson, we shall see the very basics of this theory.
1. Mean
2. Median
3. Mode
4. Range
Algebra Lesson 3
Algebra Lesson 3
Polynomial equations of small degrees are the first objects that one encounters in Algebra. In this lesson, we shall discuss the question of their solvability and also see explicit expressions for the solutions.
1. Linear equations
2. Quadratic equations
3. The discriminant of a quadratic equation.
Algebra Lesson 4
Algebra Lesson 4
The idea of telescoping products and sums is best explained with examples. Indeed, there is no general theory for these concepts so it is hard to define them rigourously. We shall see a few examples of each.
1. Telescoping sums
2. Telescoping products.
Combinatorics Lesson 1
Combinatorics Lesson 1
In this lesson, we shall describe the basic counting principles that are used in enumerative combinatorics.
1. Addition principle
2. Multiplication principle
3. Bijection principle.
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Combinatorics Lesson 2
Combinatorics Lesson 2
Permutations and combinations are, in a sense, extensions of the basic counting principles. Here we introduce the notation, discuss some basic identities and solve some problems.
1. Permutations
2. Combinations
3. Permutations with repetitions
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Combinatorics Lesson 3
Combinatorics Lesson 3
The principle of inclusion and exclusion is the last of the basic counting principles. Due to the intricacies of the statement, a separate lesson has been dedicated to it.
1. The statement of the PIE.
2. Illustrative example.
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Combinatorics Lesson 4
Combinatorics Lesson 4
The pigeonhole principle is deceptively simple; however, its applications are not. In this lesson, we shall give some formulations of the principle and use them to solve problems.
1. Two different formulations of the principles
2. Handshake theorem.
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Combinatorics Lesson 5
Combinatorics Lesson 5
Though Probability theory is an area of Mathematics in its own right, the very basics can be stated in combinatorial terms. In this lesson, we shall see the combinatorial definition of probability and some properties.
1. Sample space
2. Definition of probability
3. Conditional probability
- Opened: Monday, 28 February 2022, 12:00 AMDue: Monday, 7 March 2022, 12:00 AM
Number Theory Lesson 1
Number Theory Lesson 1
We use this lesson to revisit some basic concepts of number theory, like digits of numbers, division, and primes.
1. Decimal digits
2. Rules for checking divisibility by certain integers
3. Prime numbers
4. The greatest common divisor
5. The division algorithm
6. The Fundamental Theorem of Arithmetic
- Opened: Wednesday, 16 February 2022, 12:00 AMDue: Wednesday, 23 February 2022, 12:00 AM
Numerates