A Transition to Higher Mathematics
What you'll learn
- You will learn FUNDAMENTAL PRINCIPLES OF LOGIC in the world of mathematics
- You will learn how to PROVE THEOREMS in mathematics including DIRECT, CONTRAPOSITIVE, CONTRADICTION, INDUCTION, EXISTENCE, UNIQUENESS, PROVE WITH SETS, PROVE BY CASES, COMBINATORIAL, RECURSIVE methods
- You will learn how to prove many things including TRIGONOMETRY, CALCULUS, NUMBER THEORY, ALGEBRA, REAL ANALYSIS, GROUP THEORY and many more
- You will learn what a PROPOSITION is in mathematics
- You will learn what QUANTIFIERS are and how they work
- You will learn about PROPOSITIONAL LOGIC, including CONDITIONAL, BICONDITIONAL statements
- You will see LOGICAL CONNECTIVES such as AND, OR, XOR, NAND
- You will see PREDICATE LOGIC for expressing mathematical statements
- You will see what a VALID ARGUMENT is in mathematics
- You will learn how MATHEMATICAL INDUCTION works and how to use it to prove certain statements
- You will see THE GENERAL FRAMEWORK FOR PROVING THINGS in mathematics
- You will see THE GENERAL FRAMEWORK FOR SOLVING PROBLEMS in mathematics
- You will see what a EQUIVALENCE REDUCTION is and how it is useful
- You will see what a UNILATERAL REDUCTION is and how it is useful
- You will learn what ANALOGY is and why it is extremely useful in proving theorems and/or solving problems
- You will see what LOGICAL EQUIVALENCE is and why it is important
- You will learn HOW TO APPROACH A MATHEMATICAL PROBLEM
- You will learn CHAIN OF EQUIVALENT PROBLEMS in solving problems and proving theorems
- You will differentiate between ANALYSIS and SYNTHESIS in mathematics
Requirements
- At least high school mathematics
- Willingness to learn
- Perseverance
- Embracing failure
- Curiosity
Description
"I perfectly understand the subjects but have difficulty solving the problems or proving the theorems!"
"I understand the undergoing logic when I look at the solution/proof of a problem/theorem, but cannot think of it on my own!"
"I do not know how to prove things in mathematics!"
"I always overcomplicate the simplest mathematical concepts, and get lost easily!"
If you have a similar problem like the above ones that bothers you, THIS COURSE IS THE PERFECT CHOICE FOR YOU!
This is a perfect course for the ones who want to excel at rigorous math and who want to be a discoverer or inventor in math with a heuristic mindset!
Heuristic is the study of discovery and invention. Heuristic mindset is the basis of all discovery and invention in the history of human beings.
In this course we will see the general outline of MATHEMATICAL THINKING and MODERN HEURISTIC.
The course has 3 main parts:
Logic:
In this part we will see the basic and advanced concepts in logic that lay the foundation of building rigorous mathematical understanding and arguments.
Proofs:
Here, we will cover general proof techniques in mathematics. Proofs techniques include:
Direct proof
Proof by contraposition
Proof by contradiction
Proof by cases
Existence and uniqueness proof
Proof with sets
Proof by mathematical induction
Combinatorial proofs
Modern Heuristic:
This part includes the general steps and advices in approaching problems/theorems. We will use the steps and advices mentioned in this section combined with logic and proof techniques to learn how to solve complex problems and how to prove mathematical statements.
Possible subjects are (prone to change according to the students' feedback):
Trigonometry
Limits (Calculus)
Differentiation (Calculus)
Integration (Calculus)
Real Analysis
Analytic Geometry
Number Theory
Concept of Infinity
Complex Numbers
Group Theory
Topology
Set Theory
Combinatorics
Probability and Statistics
The course will be updated several times a month with new problems and sections according to the demand of the students. Especially Modern Heuristic section will be updated every week with new concepts and problems.
I hope you enjoy the course!
Who this course is for:
- Math Enthusiasts
- Mathematics Student
- Engineering Students
- Computer Science Students
- Computer Scientists
- Data Scientists
- Software Engineers
- Programmers
- Software Developers
- System Analysts
- Business Analysts
- Anyone who wants to be a discoverer
- Anyone who wants to be an inventor
Course content
- Preview00:00
Instructor
![Mert Atlı](data:image/svg+xml,%3Csvg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 64 64"%3E%3C/svg%3E){kind=avatar}
- 4.7 Instructor Rating
- 9 Reviews
- 320 Students
- 1 Course
Hello,
My name is Mert. I have been working as data scientist for more than 6 years. I am a master student in Software Engineering with a focus on Artificial Intelligence. I am also Statistics and Data Science Micro Master student at MIT.
I use math in my job frequently. I like solving complex business problems using machine learning and deep learning techniques with Python.
I will share my knowledge and experience on various subjects here. I hope you enjoy them!
See you then!