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Lessons

697

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Courses

10

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697

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824

Master Clustering Analysis for Data Science Using MATLAB

$200 Value

Precalculus

$200 Value

Calculus 1 Mastered

$200 Value

Master Number Base Conversion

$200 Value

Number Theory

$200 Value

Graph Theory

$200 Value

QC051: Math Prerequisites for Quantum Computing

$200 Value

Mathematical Foundation for Machine Learning & AI

$200 Value

Mathematics for Data Science & Machine Learning using R

$200 Value

Discrete Mathematics

$200 Value

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Content

4.0 hours

Lessons

26

By Nouman Azam | in Online Courses

Fully equip yourself with the art of applied machine learning using MATLAB. This course is also for you if you want to apply the most commonly used data preprocessing techniques without having to learn all the complicated maths. Additionally, this course is also for you if you have had previous hours and hours of machine learning implementation but could never figure out how to further improve the performance of the machine learning algorithms. By the end of this course, you will have at your fingertips, a vast variety of most commonly used data preprocessing techniques that you can use instantly to maximize your insight into your data set.

- Access 26 lectures & 4 hours of content 24/7
- Implement different machine learning classification algorithms using MATLAB
- Proprocess data before analysis
- Know when & how to use dimensionality reduction
- Take away code templates
- See visualization results of algorithms
- Decide which algorithm to choose for your dataset

4.4/5 Instructor Rating:
★ ★ ★ ★
★

Nouman Azam received his Ph.D. Degree in Computer Sceince from University of Regina in 2014. Prior to that, he completed his M.Sc. in Computer Software Engineering from National University of Sciences and Technology, Pakistan, and Bachelor's in Computer Sciences from National University of Computer and Emerging Sciences, Pakistan in 2007 and 2005, respectively

Nouman has over 10 years of teaching experience. He has taught almost all the major computer science subjects including introduction to computers, computer organization and architecture, operation systems, computer networks, image processing, digital logic design, discrete structures and many others. He has extensive knowledge of tools such as MATLAB, QTSpim, C++, Java and Other academic tools used for teaching and instructing purposes.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: all levels

**Requirements**

- MATLAB 2017a or heigher version. No prior knowledge of MATLAB is required

- Your First Program
- Course Introduction
- Introduction to the course - 4:07
- Code and Data used in the course

- Kmeans Clustering
- 1 - KMeans intuition - 12:18
- 2 - Choosing the right number of clusters - 15:35
- 3 - KMeans in MATLAB (Part 1) - 21:15
- 4 - KMeans in MATLAB (Part 2) - 12:57
- 5 - KMeans Limitations - (Part 1-Clusters with different sizes) - 10:30
- 6 - KMeans Limitations - (Part-2-Clusters with non spherical shapes) - 9:33
- 7 - KMeans Limitations - (Part 3-Clusters with varying densities) - 5:33

- Mean Shift Clustering
- 1 - Intuition of Mean Shift - 9:23
- 2 - Mean Shift in Python - 10:46
- 3 - Mean Shift Performance in Cases where Kmean Fails (Part 1) - 7:17
- 4 - Mean Shift Performance in Cases where Kmean Fails (Part 2) - 12:21

- DBSCAN Clustering
- 1 - Intuition of DBSCAN_DF - 9:21
- 2 - DBSCAN in matlab_DF1 - 14:39
- 3 - DBSCAN on clusters with varying sizes - 7:03
- 4 - DBSCAN on clusters with different shapes and densities - 10:57
- 5 - DBSCAN for handling noise - 7:14
- 6 - Practical Activity

- Hierarchical Clustering
- 1 - Hierarchical Clustering Intuition (Part 1)_DF - 9:50
- 2 - Hierarchical Clustering Intuition (Part 2)_DF - 15:47
- 3 - Hierarchical Clustering in Matlab - 12:21

- Applications of Clustering
- 1 - Image Compression (Part 1) - 12:43
- 2 - Image Compression (Part 2) - 7:29
- 3 - Clustering sentences (Part 1) - 14:08
- 4 - Clustering sentences (Part 2) - 11:02

Access

Lifetime

Content

21.0 hours

Lessons

118

By Miran Fattah | in Online Courses

Precalculus is a set of course that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. In this course, you will acquire skills on a wide range of functions, trigonometry, sequence and series, and conic sections. This is a place where students learn, understand, and excel in pre-calculus to have a strong foundation for more advanced courses like calculus. The course consists of an extensive curriculum that teaches about all the topics under pre-calculus.

- Access 118 lectures & 21 hours of content 24/7
- Learn to find domain & range of a variety of functions
- Learn to transform & combine functions
- Master logarithms & exponential functions
- Know how to construct & graph trigonometric functions and inverse trig functions
- Know how to prove trigonometric identities & equations
- Acquire thorough understanding on conic sections & how to find their equations.
- Determine behavior of a function from its graph
- Learn how to divide polynomials
- Master unite circle
- Determine domain & range of trigonometric functions
- Master sequence & series and get to know their different kinds
- Be able to use binomial theorem to expand powers of a binomial

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: intermediate

**Requirements**

- Very basic background in Algebra

- Fundamentals
- Number Sets - 10:17
- Coordinate Plane - 6:20

- Functions
- Function - 15:05
- Evaluating a Function - 12:29
- Domain - 15:56
- Domain of Rational Functions - 16:44
- Domain of Roots - 17:49
- Range - 5:29
- Graphs - 15:53
- Graphing Calculator - 6:09
- Piecewise Functions - 4:01
- Extracting Info from a Graph - 12:13
- Domain and Range from Graph - 7:57
- Increasing and Decreasing Functions - 7:28
- Local Maximum and Minimum - 8:41
- The Vertical Line Test - 9:46

- Function Transformations
- Vertical Shifting - 4:35
- Horizontal Shifting - 6:03
- More Examples - 9:20
- Vertical Strecthing and Shrinking - 6:27
- Horizontal stretching and shrinking - 6:24
- Graph Reflection - 10:33
- Even & Odd Functions - 8:19

- Combining Functions
- Function Combinations - 9:00
- Domain of Combined Functions - 11:52
- Function Composition - 9:43
- One-to-One Function - 8:18
- Inverse Functinos - 10:10
- Graph of Inverse Functions - 5:24
- Range Examples - 6:26

- Polynomial Functions
- Polynomials - 7:56
- End Behavior - 14:01
- Real Roots of Polynomials - 7:14
- Intermediate Value Theorem for Polynomials - 8:47
- Crossing the x-axis - 5:51
- Local Extrema - 4:31
- Long Division - 15:31
- More Examples - 7:35
- Synthetic Division - 9:00
- The Remainder Theorem - 5:44
- The Factor Theorem - 5:07
- The Rational Zeros Theorem - 12:15

- Rational Functions
- Rational Functions - 4:22
- Vertical Asymptotes - 16:01
- Horizontal Asymptotes - 10:18
- Slant Asymptotes - 11:46
- Graphing Rational Functions - 24:16

- Exponential Functions
- Exponential Functions - 4:31
- Graph of Exponential Functions - 6:48
- The Natural Exponential Function - 5:53
- Exponential Equations - 7:04
- Interest - 18:45

- Logarithmic Functions
- Logarithmic Functions - 12:38
- Graph of Logarithmic Functions - 12:28
- Natural Logarithm - 7:26
- Logarithm Laws - 6:22
- Logarithmic Equations - 8:18

- Trigonometry - Unit Circle Approach
- Introduction - 0:46
- The Unite Circle - 7:52
- Termianl Points - 30:30
- Reference Number - 21:30
- Trigonometric Functions - 12:28
- Evaluating Trigonometric Functions - 14:06
- Graph of Sine and Cosine - 24:13
- Sine & Cosine Graph Transformations - 16:31
- Tangent & Cotangent Graphs - 20:10
- Secant & Cosecant Graphs - 25:13
- Domain and Range of Sin, Cos and Tan - 21:39
- Examples - 12:47
- Domain and Range of Sec, Csc and Cot - 13:16
- Examples - 16:25

- Trigonometry - Right Triangle Approach
- Introduction - 0:42
- Angles - 15:34
- Standard Position - 7:53
- Trigonometric Ratios - 14:37
- Examples - 12:38
- Special Angles - 24:09
- Examples - 5:10
- Reference Angles - 14:13
- Evaluating Trig Functions and Points - 18:01
- Inverse Trigonometric Functions - 12:00
- The Law of Sines - 12:29
- The Law of Cosines - 9:36
- Area of a Triangle - 7:56

- Analytic Trigonometry
- Introduction - 1:25
- Fundamental Identites - 9:31
- Examples - 17:59
- Addition and Subtraction Formulas - 14:32
- Sums of Sines and Cosines - 6:48
- Double Angle Formulas - 10:06
- Half Angle Formulas - 8:05
- Formulas for Lowering Powers - 5:12
- Sum-to-Product Formulas - 5:31
- Product-to-Sum Formulas - 5:20

- Conic Sections
- Introduction - 9:23
- Circles - 3:32
- Ellipses - 26:52
- Examples - 9:27
- Parabolas - 19:37
- Examples - 12:04
- Hyperbolas - 17:44
- Examples - 14:56
- Shifted Ellipses - 18:58
- Shifted Parabolas - 14:24
- Shifted Hyperbolas - 9:34
- Polynomial - 7:56
- Polar to Rec - 10:52
- Polar Coordinates - 18:29
- Polar Equations - 6:40

- Sequence and Series
- Introduction - 0:19
- Sequnces - 6:37
- Arithmatic Sequance - 12:19
- Geometric Sequances - 8:57
- Partial Sums of Arithamtics Sequance - 11:56
- Partial Sum of Geometric Sequance - 6:31
- Series - 12:32

- The Binomial Theorem
- Factorials and Bionomial Coffiectns - 10:33
- Bionomial Theorem - 20:17

Access

Lifetime

Content

16.0 hours

Lessons

93

By Miran Fattah | in Online Courses

Calculus is the mathematical study of continuous change and the summation of infinitely many small factors. In this course, you will acquire skills to become an expert on limits, limit laws, derivatives, and their applications. This course is a place for you to learn, understand, and excel in Calculus 1 to have a strong foundation for more advanced courses like calculus 2. This course consists of an extensive curriculum that teaches different essential concepts and skills.

- Access 93 lectures & 16 hours of content 24/7
- Understand the concept & formal definition of a limit and be able to solve problems
- Learn continuity & its types
- Master the rules of derivatives
- Master related rates, optimization & linearization
- Understand L’ Hôpital’s Rule & use it to solve problems
- Comprehend the sandwich theory & be able to use it
- Learn the idea of derivatives & use it to solve problems
- Learn implicit differentiation
- Be able to properly graph functions using first & second derivative

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: intermediate

**Requirements**

- Strong background in Pre Calculus

- Supplements
- Course Overview - 3:15
- Number Sets - 10:07
- Graphing tools - 6:09

- Functions
- Intro - 0:45
- Function - 15:05
- Evaluating a Function - 12:29
- Extracting Info from a Graph - 12:13
- Domain - 15:56
- Range - 5:29
- Function Composition - 9:43
- Function Combination - 9:00
- Even and Odd function - 8:19
- One-to-One Function - 8:18
- Inverse Functinos - 10:10
- Exponential Functions - 4:31
- The Natural Exponential Function - 5:53
- Logarithms - 12:38
- Natural Logarithms - 7:26
- Logarithm Laws - 6:22
- Trigonometric Ratios - 14:37
- Evaluating Trig Functions and Points - 18:01
- Inverse Trigonometric Functions - 12:00

- Limits
- Intro - 0:25
- What is a Limit? - 17:03
- Examples - 14:53
- One-Sided Limits - 11:34
- Limit Laws - 7:56
- Examples - 14:31
- More Examples - 14:30
- The Squeeze (Sandwich) Theorem - 9:53
- Examples - 9:53
- Percise definition of a Limit - 8:10
- Examples - 14:48
- Limits at Infinity - 20:31
- Examples - 14:41
- Asymptotes and Limits at Infinity - 10:18
- Infinit Limits - 12:00

- Continuity
- Intro - 0:24
- Continuty - 11:32
- Types of Discontinuity - 11:38
- Examples - 16:56
- Properties of Continues Functions - 10:41
- Intermediate Value Theorem - 6:18

- Derivatives
- Intro - 0:41
- Average Rate of Change - 8:57
- Instantaneous Rate of Change - 11:49
- Derivative Definition - 13:37
- Examples - 10:28
- Non Differentiable Functions - 6:16
- Constant and Power Rule - 8:33
- Constant Mulitple Rule - 6:32
- Sum and Difference Rule - 6:34
- Product Rule - 13:39
- Quotent Rule - 8:03
- Chain Rule - 14:04
- Examples - 8:46
- Derivative Symbols - 4:11
- Graph of Derivatives - 10:21
- Higher Order Derivatives - 7:39
- Equation of the Tangent Line - 7:23
- Derivative of Trig Functions - 6:53
- Examples - 19:24
- Derivative of Inverse Trig Functions - 8:16
- Examples - 11:40
- Implicit Difrentiation - 16:40
- Derivative of Inverse Functions - 12:47
- Derivative of the Natural Exponential Function - 11:14
- Derivative of the Natural Logarithm Function - 7:02
- Derivative of Exponential Functions - 6:03
- Derivative of Logarithmic Functions - 6:18
- Logarithmic Differentiation - 14:36

- Application of Derivatives
- Intro - 0:46
- Related Rates - 8:25
- Example - 13:03
- Example - 9:24
- Example - 10:18
- Optimization - 15:34
- Example - 11:11
- Example - 7:20
- Extreme Values of Functions - 11:32
- Critical Points - 7:38
- Examples (First Derivative Test) - 15:42
- More Examples - 17:41
- Concavity - 8:28
- Examples - 12:36
- Second Derivative Test - 7:57
- Graphing Functions - 21:12
- Examples - 17:06
- L’ Hôpital’s Rule - 11:31
- Other Indeterminate Forms - 15:12
- Rolle's Theorem - 9:17
- Mean Value Theorem - 18:48
- Mean Value Theorem Application - 3:32

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Lifetime

Content

1.0 hours

Lessons

12

By Miran Fattah | in Online Courses

Number bases are different ways of writing and using the same number. In this course, you will learn what number bases are as well as the different important number bases like Base 2, 8, and 16. You will also learn how to convert from base 10 to base 2, 8, and 16 and back. Number bases are very important as it is one of the skills useful to programmers. When you understand how numbers are represented in base 2 (Binary), base 8 (Octal), and base 16 (Hexadecimal), you will better understand different aspects of programming.

- Access 12 lectures & 1 hour of content 24/7
- Know how to convert decimal base to binary base & vice versa
- Know how to convert decimal base to hexadecimal base & vice versa
- Learn how to do arithmetics in binary, octal, & hexadecimal base
- Know how to convert decimal base to octal base & vice versa
- Learn how to convert any base to base 10 & back
- Get to know the different number sets

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: beginner

**Requirements**

- Know base 10 (Decimal base)
- Know how to do Arithmetics ( +, –, x, ÷) in base 10

- Introduction
- Number Sets - 8:50
- Number Bases - 11:33

- Base 2
- Binary Base - 11:36
- More Examples - 7:34
- Binary Arithmetics - 15:17

- Base 8
- Octal Base - 7:47
- More Example - 4:10
- Octal Arithmetics - 13:24

- Base 16
- Hexadecimal Base - 13:13
- More Example - 6:20
- Hexadecimal Arithmetics - 14:18

- Conclusion
- From any base to base 10 and back - 5:55

Access

Lifetime

Content

8.0 hours

Lessons

63

By Miran Fattah | in Online Courses

Number theory is the study of patterns, relationships, and properties of numbers. Studying numbers is a part theoretical and a part experimental, as mathematicians seek to discover fascinating and unexpected mathematical relationships and properties. In this course, you will explore some of those fascinating mathematical relationships and properties and you will learn essential topics that are in the heart of Mathematics, Computer Science, and many other disciplines.

- Access 63 lectures & 8 hours of content 24/7
- Gain thorough understanding of number theory
- Know different number bases like binary & hexadecimal
- Master divisibility & its rules, Euclidean division theorem, and others
- Know the fundamental theorem of Arithmetic
- Learn about finite, infinite, & periodic continued fractions
- Know different numbers, number sets, patterns, & properties
- Master factorials, double factorials, factorions, & more
- Learn about primes, prime powers, factorial primes, & Euclide's first theorem
- Master modular arithmetics
- Explore public key cryptography, diffie-hellman protocol, & RSA encryption

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: beginner

**Requirements**

- Know basic arithmetic operations like +, -, x and ÷ (including long division)
- Know what is a matrix

- Basics
- What is Number Theory - 7:36
- Number Sets - 10:07
- Number Patters - 10:00
- Even and Odd - 11:05
- Number Properties - 9:58
- Proofs - 11:23

- Number Bases
- Number Bases - 11:33
- Binary Base - 11:36
- More Examples - 7:34
- Binary Arithmetics - 15:17
- Hexadecimal Base - 13:13
- Hexadecimal Arithmetics - 14:18

- Factorials
- Factorial - 5:01
- Double Factorial - 8:47
- Super Factorial - 2:32
- Exponential Factorial - 2:42
- Factorion - 5:22
- Stirling's Formula - 3:20
- Number of Digits - 2:37

- Divisibility
- Divisibility - 7:01
- Divisibility Rules - 4:21
- Euclidean Division Theorem - 8:26
- GCD & LCM - 10:33
- Bezout's Identity - 7:41
- Perfect Number - 3:41
- Practical Numbers - 5:08
- Amicable Numbers - 3:43
- Fibonacci Sequence - 8:40
- Tribonacci Sequence - 5:23
- Golden Ratio - 10:42

- Primes
- Prime Numbers - 8:56
- Fundamental Theorem of Arithmetics (FTA) - 9:58
- Almost Primes - 7:15
- Prime Powers - 1:45
- Factorial Prime - 2:59
- Euclid's Theorems - 8:47
- The Prime Number Theorem (PNT) - 3:48
- Unsolved Problems - 6:18
- NumberEmpire - 7:26

- Modular Arithmetics
- Modular Arithmetics - 8:49
- Congruence - 13:07
- Congruence Class - 11:33
- Residue Systems - 4:10
- Quadratic Residues - 4:12
- Module Operations - 6:10
- Inverses - 6:58
- Modular Exponentiation - 10:02
- Wilson’s Theorem - 5:08
- Chinese Remainder Theorem - 9:29
- Fermat's Little Theorem - 4:39
- Euler's Totient Function - 6:46
- Euler-Fermat Theorem - 3:47

- Continued Fractions
- Continued Fraction - 8:19
- Negative Continued Fraction - 10:51
- Finite Continued Fractions - 14:05
- Infinite Continued Fractions - 16:48
- Periodic Continued Fractions - 9:32
- Convergent - 11:57

- Cryptography
- Cryptography - 8:45
- Early Cyphers - 11:18
- Public Key Cryptography - 12:32
- RSA Encryption - 10:52
- Diffie-Hellman Protocol - 4:28

Access

Lifetime

Content

9.0 hours

Lessons

66

By Miran Fattah | in Online Courses

Graph theory is an advanced topic in mathematics that deals with the fundamentals and properties of a graph. The course consists of several sections and in each section, there are video lectures where few concepts are explained. There is an example(s) after the explanation(s) so you understand the material more. After every lecture, there are quizzes (with solutions) so you can test what you have learned in that lecture.

- Access 66 lectures & 9 hours of content 24/7
- Master fundamental concepts in graph theory
- Know different graphs & their properties
- Understand graph coloring
- Obtain solid foundation in trees, tree traversals & expression trees
- Understand Eulerian & Hamilton paths and circuits
- Perform elementary & advanced operations on graphs
- Know how to turn a graph into a matrix & vice versa

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: advanced

**Requirements**

- Knowledgeable on elementary operations like addition & mutliplication

- Supplements
- Course Overview - 3:24
- TextBook Recommendations - 2:21
- Tools and Softwares - 5:26
- Sets - 8:38
- Number Sets - 10:07
- Parity - 12:24
- Terminologies - 7:15

- Fundamentals
- Graphs Intro - 2:45
- Graphs - 11:25
- Subgraphs - 8:32
- Degree - 9:52
- Sum of Degrees of Vertices Theorem - 23:22
- Adjacency and Incidence - 9:15
- Adjacency Matrix - 16:16
- Incidence Matrix - 8:04
- Isomorphisms - 8:23

- Paths
- Intro - 0:36
- Walks, Trails, Paths, and Circuits - 12:35
- Examples - 10:18
- Eccentricity, Diameter, and Radius - 6:47
- Connectedness - 20:03
- Euler Trails and Circuits - 17:36
- Fleury’s Algorithm - 10:15
- Hamiltonian Paths and Circuits - 5:46
- Ore's Theorem - 14:08
- Dirac's Theorem - 6:05
- The Shortest Path Problem New New - 15:57

- Graph Types
- Intro - 0:32
- Trivial, Null, and Simple Graphs - 9:29
- Regular Graphs - 9:35
- Complete, Cycles and Cubic Graphs - 10:01
- Path, Wheel and Platonic Graphs - 10:34
- Bipartite Graphs - 14:15

- Trees
- Intro - 0:31
- Trees - 14:02
- Cayley's Theorem - 2:59
- Rooted Trees - 10:24
- Binary Trees - 13:46
- Binary Tree Traversals - 18:04
- Binary Expression Trees - 8:54
- Binary Search Trees (BST) - 19:23
- Spanning Trees - 10:01
- Forest - 7:28

- Digraphs and Tournaments
- Intro - 0:20
- Digraphs - 11:58
- Degree Digraph - 9:07
- Isomorphism Digraphs - 7:30
- Adjacency Matrix Digraphs - 10:16
- Incidence Matrix Digraph - 4:50
- Walks, Paths and Cycles Digraphs - 12:06
- Connectedness Digraph - 5:22
- Tournaments - 7:47

- Planar Graphs
- Intro - 0:21
- Planar Graphs - 9:52
- Kuratowski's Theorem - 14:05
- Euler's Formula - 10:26
- Dual Graphs - 10:55

- Graph Operations
- Intro - 0:35
- Vertex and Edge Deletion - 7:32
- Cartesian Product - 9:46
- Graph Join and Transpose - 4:01
- Complement Graphs - 5:17

- Graph Colorings
- Intro - 0:21
- Vertex Colorings - 5:26
- Edge Colorings - 8:43
- Total Colorings - 5:24

Access

Lifetime

Content

4.0 hours

Lessons

112

By Kumaresan Ramanathan | in Online Courses

This *QC051: Math Prerequisites for Quantum Computing* course is a 4-hour refresher course that will review the Math you will need to understand quantum computing concepts. With 112 lectures, this course covers the topics of probability, statistics, boolean logic, complex numbers, and linear algebra. To get the most out of this course, you need to have already studied Math at a 12th grade level in high-school.

- Access 112 lectures & 4 hours of content 24/7
- Review probability, statistics, boolean logic, complex numbers, and linear algebra
- Refresh 12th grade Math topics to prepare for quantum computing

4.4/5 Instructor Rating
★

Kumaresan Ramanathan has taught students at the University of Massachusetts and guided software professionals at Cadence Design Systems, iCOMS, Empirix, Relona, and Johnson & Johnson. His courses help beginners who have a basic understanding of high school Math and coding.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: beginner

**Requirements**

- 12th grade Math & Physics

- Boolean Algebra
- Introduction - 4:18
- Boolean Algebra - 4:43
- Boolean Variables and Operators - 7:09
- Truth Tables - 3:17
- Logic Gates - 1:22
- Logic Circuits - 0:52
- AND - 0:58
- OR - 0:51
- NOT - 1:03
- Multiple Input Gates - 1:35
- Equivalent Circuits 1 - 1:59
- Equivalent Circuits 2 - 0:59
- Universal Gate : NAND - 2:56
- Exclusive-OR - 2:17
- XOR for Assignment - 2:03
- XOR of Bit Sequences 1 - 2:40
- XOR of Bit Sequences 2 - 4:21

- Cryptography
- Introduction to Cryptography - 1:50
- Cryptography with XOR - 2:34
- Shared Secret - 2:35
- Importance of Randomness - 1:25
- Breaking the Code - 5:34

- Probability
- Introduction to Probability - 5:08
- Probability of a Boolean Expression - 1:42
- Mutually Exclusive Events - 3:01
- Independent Events - 1:16
- Manipulating Probabilities with Algebra - 2:24
- P ( Mutually Exclusive Events ) - 0:53
- P ( Independent Events ) - 1:17
- Complete Set of Mutually Exclusive Events - 2:00
- P ( A OR B ) - 1:35
- Examples - 0:51
- Examples - 7:53
- P ( Bit Values ) - 3:56
- Analysis with Venn Diagrams - 1:27
- Venn Diagram P ( A AND B ) - 0:53
- Venn Diagram P ( A OR B ) - 1:09
- Venn Diagram P ( NOT A ) - 0:34
- Examples - 2:42
- Examples - 2:35
- Conditional Probability - 2:06
- Examples - 1:28

- Statistics
- Introduction to Statistics - 1:21
- Random Variables - 1:33
- Mapping Random Variables - 4:20
- Mean, Average, Expected Value ... - 1:49
- Example - 2:23
- Example - 1:37
- Beyond Mean - 1:46
- Standard Deviation - 3:50
- Examples - 4:15
- Combinations of Random Variables - 2:53
- Correlation - 2:36
- Analysis of Correlation - 6:19

- Complex Numbers
- Introduction to Complex Numbers - 5:07
- Imaginary i - 4:55
- Addition - 1:54
- Subtraction - 1:08
- Multiplication by a Real - 0:55
- Division by a Real - 0:41
- Complex Multiplication - 2:30
- Examples - 1:26
- Complex Conjugates - 1:37
- Squared Magnitude - 2:12
- Complex Division - 3:01
- Examples - 1:12
- Euler's Formula - 2:15
- Polar Form - 2:44
- Examples - 2:43
- Fractional Powers - 3:24
- Complex Cube Roots of 1 - 1:30
- Square Root of i - 1:29
- 2D Coordinates - 3:00

- Linear Algebra & Matrices
- Matrices - 1:36
- Matrix Dimensions - 2:13
- Matrix Addition - 1:42
- Matrix Subtraction - 1:12
- Scalar Multiplication - 1:12
- Matrix Multiplication - 7:40
- Examples - 0:59
- Examples - 0:41
- 3x3 Example - 0:59
- Exercises - 0:33
- More Multiplications - 0:57
- When is Multiplication Possible ? - 2:06
- Example - 1:23
- Not Commutative - 1:52
- Associative & Distributive - 1:25
- Dimension of Result - 2:22
- Odd Shaped Matrices - 1:03
- Examples - 1:01
- Outer Product - 1:46
- Exercises - 0:21
- Inner Product - 1:43
- Exercises - 0:41
- Identity Matrix - 2:15
- Matrix Inverse - 2:46
- Transpose - 1:21
- Transpose Examples - 1:00
- Transpose of Product - 1:16
- Complex Conjugate of Matrices - 1:19
- Adjoint - 1:07
- Unitary - 1:45
- Hermitian - 1:08
- Hermitian & Unitary - 1:37
- Why Hermitian or Unitary ? - 0:57
- Vectors & Transformations - 4:50
- Rotation in 2D - 1:51
- Special Directions - 3:59
- Eigen Vectors & Eigen Values - 4:35
- More Eigen Vectors - 2:58
- Conclusion - 0:51

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Content

4.0 hours

Lessons

18

By Eduonix Learning Solutions | in Online Courses

With self-driving cars on the road and virtual assistants inside our phones, it's clear we're moving toward an AI-powered future. As such, demand is high for those who understand the science that powers these innovations, and this course can help you join their ranks. Designed with the beginner in mind, this course will give you the mathematical foundation required for writing programs and algorithms for AI and machine learning. You'll explore linear algebra, multivariate calculus, and probability theory, and emerge ready to put these algorithms to use in your own AI projects.

- Access 18 lectures & 4 hours of content 24/7
- Explore the core mathematical concepts for machine learning
- Learn how to implement machine learning concepts with R & Python
- Understand how neural networks are put together & how they operate

Eduonix creates and distributes high-quality technology training content. Their team of industry professionals has been training manpower for more than a decade. They aim to teach technology the way it is used in the industry and professional world. They have a professional team of trainers for technologies ranging from Mobility, Web and Enterprise, and Database and Server Administration.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: all levels

**Requirements**

- Background in Algebra

- Introduction
- Introduction - 3:52

- Linear Algebra
- Scalars, Vectors, Matrices, and Tensors - 21:14
- Vector and Matrix Norms - 9:35
- Vectors, Matrices, and Tensors in Python - 21:27
- Special Matrices and Vectors - 13:35
- Eigenvalues and Eigenvectors - 11:41
- Norms and Eigendecomposition - 28:21

- Multivariate Calculus
- Introduction to Derivatives - 19:24
- Basics of Integration - 11:08
- Gradients - 12:05
- Gradient Visualization - 18:49
- Optimization - 18:51

- Probability Theory
- Intro to Probability Theory - 11:00
- Probability Distributions - 10:13
- Expectation, Variance, and Covariance - 11:23
- Graphing Probability Distributions in R - 12:31
- Covariance Matrices in R - 9:49

- Probaility Theory
- Special Random Variables - 10:52

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Content

10.0 hours

Lessons

65

By Eduonix Learning Solutions | in Online Courses

Data Science has become one of the most important aspects in most of the fields. From healthcare to business, data is important. However, it revolves around 3 major aspects and these are data, foundational concepts, and programming languages for interpreting the data. In this course, you will be taught about foundational mathematics for Data Science using R programming language, a language developed specifically for performing statistics, data analytics, and graphical modules in a better way.

- Access 65 lectures & 10 hours of content 24/7
- Master the fundamental mathematical concepts required for data science & machine learning
- Master linear algebra, calculus & vector calculus from ground up
- Learn to implement mathematical concepts using R programming language
- Master R programming language

Eduonix creates and distributes high-quality technology training content. Their team of industry professionals has been training manpower for more than a decade. They aim to teach technology the way it is used in the industry and professional world. They have a professional team of trainers for technologies ranging from Mobility, Web and Enterprise, and Database and Server Administration.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: intermediate

**Requirements**

- Very basic background in Algebra

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: intermediate

**Requirements**

- Basic knolwedge on statistics & mathematics

- Introduction
- Intro - 1:01

- Overview of R
- Introduction - 2:02
- Overview of R Workspace & Basic Commands - 22:50
- LAB 1 Intro - 2:27
- LAB 1 Solution - 11:10

- Linear Algebra
- Scalars Vectors and Matrices - 12:15
- Application Scalars Vectors and Matrices - 18:41
- LAB 1 Intro Scalars Vectors and Matrices - 1:38
- LAB 1 Solution Scalars Vectors and Matrices - 12:15
- Vector Operations - 11:59
- Application Vector Operations - 22:10
- LAB 2 Intro Vector Operations - 1:54
- LAB 2 Solution Vector Operations - 11:55
- Matrix Operations Addition Subtraction Multiplication - 17:40
- Application Matrix Operations Addition Subtraction Multiplication - 11:08
- LAB 3 Intro Matrix Operations Addition Subtraction Multiplication - 1:12
- LAB 3 Solution Matrix Operations Addition Subtraction Multiplication - 4:07
- Matrix Operations Transposes and Inverses - 11:33
- Application Matrix Operations Transposes and Inverses - 12:54
- LAB 4 Intro Matrix Operations Transposes and Inverses - 1:00
- LAB 4 Solution Matrix Operations Transposes and Inverses - 3:19
- What is Linear Regression - 11:27
- Application What is Linear Regression - 28:05
- LAB 5 Intro What is Linear Regression - 2:17
- Lab 5 Solution What is Linear Regression - 12:12
- Matrix Representation of Linear Regression - 12:28
- Application Matrix Representation of Linear Regression - 13:37
- Lab 6 Intro Matrix Representation of Linear Regression - 3:21
- Lab 6 Solution Matrix Representation of Linear Regression - 12:45

- Section Calculus
- Functions and Tangent Lines - 15:31
- Application Functions and Tangent Lines - 18:31
- Lab 1 Intro Functions and Tangent Lines - 1:51
- Lab 1 Solution Functions and Tangent Lines - 13:12
- Derivatives - 9:50
- Application Derivatives - 18:35
- Lab 2 Intro Derivatives - 2:38
- Lab 2 Solution Derivatives - 14:58
- Optimization Using Derivatives Single Variable Functions - 11:58
- Application Optimization Using Derivatives Single Variabl - 10:22
- Intro Optimization Using Derivatives Single Variable Function - 1:26
- Lab 3 Solution Optimization Using Derivatives Single Variable Funct - 8:15
- Optimization Using Derivatives Two Variable Functions - 10:42
- Application Optimization Using Derivatives Two Variable F - 17:03
- Lab 4 Intro Optimization Using Derivatives Two Variable Functions - 2:25
- Lab 4 Solution Optimization Using Derivatives Two Variable Function - 5:02
- Linear Regression The Calculus Optimization Perspective - 19:59
- Application Linear Regression The Calculus Optimization P - 16:41
- Lab 5 Intro Linear Regression The Calculus Optimization Perspective - 2:56
- Lab 5 Solution Linear Regression The Calculus Optimization Perspect - 14:26

- Tying it All Together Vector Calculus
- Orthogonal Vectors and Linear Independence - 10:32
- Application Orthogonal Vectors and Linear Independence - 13:15
- Lab 1 Intro Orthogonal Vectors and Linear Independence - 2:47
- Lab 1 Solution Orthogonal Vectors and Linear Independence - 12:07
- Eigenvectors and Eigenvalues - 12:47
- Application Eigenvectors and Eigenvalues - 9:50
- Lab 2 Intro Eigenvectors and Eigenvalues - 0:49
- Lab 2 Solution Eigenvectors and Eigenvalues - 4:42
- Vectors Gradient Descent - 10:02
- Application Vectors Gradient Descent - 10:51
- Lab 3 Intro Vectors Gradient Descent - 1:21
- Lab 3 Solution Vectors Gradient Descent - 12:50
- Linear Regression The Gradient Descent Perspective - 4:17
- Application Linear Regression The Gradient Descent Perspective - 17:55
- Lab 4 Intro Linear Regression The Gradient Descent Perspectivve - 1:15
- Lab 4 Solution Linear Regression The Gradient Descent Perspective - 7:20

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Content

19.0 hours

Lessons

124

By Miran Fattah | in Online Courses

Discrete Mathematics is the backbone of Mathematics and Computer Science. It's the study of topics that are discrete rather than continuous, for that, the course is a MUST for any Math or SC student. This course covers the most essential topics that will touch every Math and Science student at some point in their education. Discrete Mathematics gives students the ability to understand the Math language and based on that, the course is divided into 8 sections: Sets, Logic, Number Theory, Proofs, Functions, Relations, Graph Theory, Statistics, and Combinatorics.

- Access 124 lectures & 19 hours of content 24/7
- Learn the language of Mathematics & Mathematical symbols
- Construct, read & prove Mathematical statements using a variety of methods
- Understand the fundamental topics in Logic, how to construct truth tables, & tell the falsehood or truthfulness of compound statements
- Understand Boolean Expressions, black boxes, logical gates, digital circuits & many related topics
- Master fundamentals of Set Theory, equivalence relations & equivalence classes
- Learn the fundamental theorem of arithmetic
- Find incidence & adjacency matrices, and identify walks trails, paths and circuits
- Learn essential concepts in Statistics & Combinatorics

4.4/5 Instructor Rating
★

Fattah has a B.S. in Mathematics and Geophysics from theUniversity of Oklahoma in Oklahoma, USA. He has taught and tutored many college students both in the United States and Iraq. His love for teaching made him one of four students in Iraq to receive a full scholarship to pursue a B.S. degree in the States to return to his home country and teach. He is passionate about Math & Science and loves to share his passion with others. To him, Mathematics and Sciences are crucial for everyone to learn no matter how little. He is a BIG believer in visual learning, and he aims to deliver the concepts easily and directly to make the learning process fast for everyone.

**Important Details**

- Length of time users can access this course: lifetime
- Access options: desktop & mobile
- Certificate of completion included
- Redemption deadline: redeem your code within 30 days of purchase
- Updates included
- Experience level required: all levels

**Requirements**

- A fair background in algebra

- Sets
- Introduction - 0:19
- Defenition of a Set - 8:41
- Number Sets - 10:07
- Set Equality - 9:16
- Set-Builder Notation - 9:56
- Types of Sets - 11:49
- Subsets - 10:27
- Power Set - 5:06
- Ordered Pairs - 4:59
- Cartesian Products - 14:08
- Cartesian Plane - 3:38
- Venn Diagrams - 3:13
- Set Operations (Union, Intersection) - 14:35
- Properties of Union and Intersection - 10:16
- Set Operations (Difference, Complement) - 11:57
- Properties of Difference and Complement - 7:29
- De Morgan’s Law - 8:17
- Partition of Sets - 15:49

- Logic
- Introduction - 0:22
- Statments - 7:13
- Compound Statements - 13:10
- Truth Tables - 9:20
- Examples - 13:03
- Logical Equivalence - 6:39
- Tautologies and Contradictions - 6:15
- De Morgan’s Laws in Logic - 11:34
- Logical Equivalence Laws - 3:23
- Conditional Statements - 12:58
- Negation of Conditional Statements - 9:31
- Converse and Inverse - 7:25
- Biconditional Statements - 8:46
- Examples - 11:50
- Digital Logic Circuits - 12:54
- Black Boxes and Gates - 15:18
- Boolean Expressions - 6:23
- Truth Tables and Circuits - 9:24
- Equivalent Circuits - 6:37
- NAND and NOR Gates - 7:12
- Quantified Statements-ALL - 7:36
- Quantified Statements-ANY - 6:39
- Negations of Quantified Statements - 8:28

- Number Theory
- Introduction - 0:35
- Parity - 12:43
- Divisibility - 10:45
- 44-Prime Numbers - 8:03
- 45-Prime Factorization - 8:33
- GCD, LCM - 17:23

- Proofs
- Proofs - 5:40
- Terminologies - 7:37
- Direct Proofs - 8:45
- Proof by Contraposition - 11:26
- Proofs by Contradiction - 17:16
- Proofs by Exhaustion - 13:36
- Existence & Uniqueness Proofs - 15:57
- Proofs by Induction - 11:41
- Induction Examples - 18:46

- Functions
- Introduction - 0:24
- Functions - 15:05
- Evaluating a Function - 12:29
- Domain - 15:56
- Range - 5:29
- Function Composition - 9:43
- Function Combination - 9:00
- Even and Odd function - 8:19
- One-to-One Function - 8:18
- Inverse Functinos - 10:10

- Relations
- Introduction - 0:25
- The Language of Relations - 10:26
- Relations on Sets - 12:44
- The Inverse of a Relation - 6:05
- Reflexivity, Symmetry, and Transitivity - 13:07
- Examples - 7:31
- Properties of Equality & Less Than - 7:48
- Equivalence Relation - 6:42
- Equivalence Class - 6:30

- Graph Theory
- Introduction - 0:28
- Graphs - 11:25
- Subgraphs - 8:32
- Degree - 9:52
- Sum of Degrees of Vertices Theorem - 23:22
- Adjacency and Incidence - 9:15
- Adjacency Matrix - 16:16
- Incidence Matrix - 8:04
- Isomorphisms - 8:23
- Walks, Trails, Paths, and Circuits - 12:41
- Examples - 10:18
- Eccentricity, Diameter, and Radius - 6:47
- Connectedness - 20:03
- Euler Trails and Circuits - 17:36
- Fleury’s Algorithm - 10:15
- Hamiltonian Paths and Circuits - 5:46
- Ore's Theorem - 14:08
- The Shortest Path Problem - 12:58

- Statistics
- Introduction - 0:19
- Terminologies - 3:05
- Mean - 3:31
- Median - 3:11
- Mode - 3:01
- Range - 8:00
- Outlier - 4:18
- Variance - 9:25
- Standard Deviation - 4:14

- Combinatorics
- Introduction - 3:29
- Factorials! - 7:46
- The Fundamental Counting Principle - 13:24
- Permutations - 12:50
- Combinations - 12:01
- Pigeonhole Principle - 6:10
- Pascal's Triangle - 8:20

- Sequence and Series
- Introduction - 0:19
- Sequnces - 6:37
- Arithmatic Sequance - 12:19
- Geometric Sequances - 8:57
- Partial Sums of Arithamtics Sequance - 11:56
- Partial Sum of Geometric Sequance - 6:31
- Series - 12:32

- Unredeemed licenses can be returned for store credit within 30 days of purchase. Once your license is redeemed, all sales are final.