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2021-02-27 06:13:34
30-Day Money-Back Guarantee
Teaching & Academics Math

A Transition to Higher Mathematics

Learn How to Think, Solve Problems, and Prove Theorems Like a Mathematician!
Rating: 4.9 out of 54.9 (7 ratings)
294 students
Created by Mert Atlı
Last updated 9/2020
English
English [Auto]
30-Day Money-Back Guarantee

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:

  1. 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.


  2. Proofs:

    Here, we will cover general proof techniques in mathematics. Proofs techniques include:

    1. Direct proof

    2. Proof by contraposition

    3. Proof by contradiction

    4. Proof by cases

    5. Existence and uniqueness proof

    6. Proof with sets

    7. Proof by mathematical induction

    8. Combinatorial proofs


  3. 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

13 sections • 47 lectures • 4h 24m total length

  • Preview00:00

  • Preview00:32
  • Preview03:32
  • Quiz: Introduction to Logic
    3 questions

  • Propositional Logic
    06:49
  • Preview04:45
  • Conditional Statement Problem with Solutions
    00:00
  • Biconditional Statement Problem with Solutions
    00:00
  • Converse, Contrapositive, and Inverse Problem with Solution
    00:00
  • Quiz: Propositional Logic
    7 questions
  • Truth Tables
    02:39
  • Truth Tables
    3 questions
  • Truth Table Construction
    02:08
  • Truth Tables: Problems with Solutions
    00:00
  • Assignment 1
    9 questions

  • Logical Equivalences
    03:43
  • Logical Equivalences
    5 questions
  • Logical Equivalences in Actions
    03:54
  • Quiz: Logical Equivalences
    4 questions
  • Preview09:28
  • Assignment 2
    6 questions
  • Computer Scientists Attempt to Corner the Collatz Conjecture
    00:43
  • Mathematician Proves Huge Result on ‘Dangerous’ Problem
    00:14
  • Functionally Completeness
    09:40
  • NAND(|) and NOR(↓) Operators
    07:10

  • Preview01:24
  • Milestone Quiz
    6 questions

  • Predicates and Quantifiers
    06:52
  • Summary and Examples
    12:42
  • Quiz: Predicates and Quantifiers
    6 questions

  • Nested Quantifiers
    08:15
  • Negating Nested Quantifiers
    02:25
  • Uniqueness Expression
    3 questions
  • Summary and Examples
    13:17

  • Preview01:14

  • Logical Inference
    08:50
  • Rules of Inference
    4 questions
  • Resolution Principle
    07:18
  • Resolution Principle
    4 questions
  • Inference for Quantified Statements
    04:44
  • Inference Overall
    3 questions

  • Preview00:43

Instructor

Mert Atlı
Data Scientist in Worldwide Telecommunication Company
Mert Atlı
  • 4.9 Instructor Rating
  • 7 Reviews
  • 294 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!

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