Fundamental Concepts of Mathematics for Computer Science

Name: Fundamental Concepts of Mathematics for Computer Science
Rating: 4.3 (5 reviews)

Definitions & Proofs, Sets & Functions, Relations Discrete Structures, Graphs Theory, Counting principles.

Created byEdu Career College

Last updated 1/2023

English

What you'll learn

Doing the problem sets is for most students, the best way to master the course material. Problem sets will count for up to 30% of the final grade.
Use logical notation to define and reason about fundamental mathematical concepts such as sets, relations, functions, and integers.
Fundamental Concepts of Mathematics: Definitions, Proofs, Sets, Functions, Relations, Discrete Structures, Modular Arithmetic, Graphs, State machines, Counting
Discrete Mathematics principles of discrete probability to calculate probabilities and expectations of simple random processes.
Mathematically about basic data types and structures (such as numbers, sets, graphs, and trees) used in computer algorithms and systems).
Apply graph theory models of data structures and state machines to solve discrete math of connectivity and constraint satisfaction, for example, scheduling.
Evaluate elementary mathematical arguments and identify fallacious reasoning (not just fallacious conclusions).

Course content

2 sections • 12 lectures • 1h 52m total length

Reading/Notes Week 1 - Pythagorean theorem and A False proof
Video Week 1 - Pythagorean theorem and A False proof12:13
This math video provides a basic introduction into the False proof pythagorean theorem. It explains how to find the missing side length of a right triangle in addition to finding the length of each side of a triangle with variables of x.
Assignment Week 1 - Set 1
Reading/Notes, Week 2 - Predicates & Sets / + Induction
Video Week 2 - Predicates & Sets / + Induction18:07
This video provides a basic introduction into mathematical induction. It contains plenty of examples and practice problems on mathematical induction proofs. It explains how to prove certain mathematical statements by substituting n with k and the next term k + 1. Examples include arithmetic sequences and exponents.
Assignment Week 2 - Set 2
Reading/Notes, Week 3 - Binary Relations
Assignment Week 3 - Set 3
Reading/Notes - Week 4: Graph Theory
Assignment Week 4 - Set 4

Reading/Notes - Week 5 - Introduction to Number Theory
Assignment Week 5 - Set 5
Reading/Notes - Week 6 - State Machines: Invariants Fallacies with Infinity
Assignment Week 6 - Set 6
Reading/Notes - Week 7 - Counting 1 & Counting 2
Assignment Week 7 - Set 7
Reading/Note - Week 8 - Generating Functions53:44
This video provides a basic introduction into the representation of Generating functions as power series. It explains how to represent a function as a power series centered at 0 and centered at some value c. It also explains how to approximate function values using geometric power series. This video also explains how to find the radius of convergence and the interval of convergence of a geometric power series. To write a power series from a function, you need to write the function in the form of the formula for the infinite sum of a geometric series. To find the interval of convergence, find the common ratio represented by some variable expression of x and set it less than 1 and solve the inequality. This video also includes examples and practice problems of adding and subtracting power series as well as using partial fraction decomposition.
Assignment Week 8 - Set 8
Reading/Note - Week 9 - Introduction to Probability16:58
This video provides an introduction to probability. It explains how to calculate the probability of an event occuring. It also discusses how to determine the sample space of an event using tree diagrams.
Assignment Week 9 Set - 9
Reading/Notes 1-2 Week 10 - Random Variables, Distributions & Missed Expectation11:45
This videos provides a basic introduction into Random Variables probability density functions. It explains how to find the probability that a continuous random variable such as x in somewhere between two values by evaluating the definite integral from a to b. The probability is equivalent to the area under the curve. This video also contains an example problem with an exponential density function involving the mean u which represents the average wait time for a customer in the example problem.
Assignment Week 10 - Set 10

Requirements

No computer programming experience needed. You should be familiar with sequences and series, limits, and integration and differentiation of univariate functions.

Description

In this course, students will learn the fundamental principles of discrete mathematics as they relate to computer science. Discrete mathematics is a branch of mathematics that deals with discrete, rather than continuous, objects. It is an essential tool in computer science, as it provides the mathematical foundations for the design and analysis of algorithms, software engineering, and computer systems.

Upon completing the course, students will be able to understand and apply the basic methods of discrete mathematics, including set theory, logic, combinatorics, and graph theory. These methods will enable them to analyze and solve problems related to the design and analysis of algorithms, as well as the development and operation of software and computer systems.

In addition to acquiring a strong foundation in discrete mathematics, students will also develop skills in problem-solving and critical thinking, which are crucial for success in computer science and other fields. By learning to think logically and systematically, students will be better prepared to tackle complex challenges and make informed decisions in their future careers.

In particular, students will be able to:

Reason mathematically about basic data types and structures (such as numbers, sets, graphs, and trees) used in computer algorithms and systems; distinguish rigorous definitions and conclusions from merely plausible ones; synthesize elementary proofs, especially proofs by induction.
Model and analyze computational processes using analytic and combinatorial methods.
Apply principles of discrete probability to calculate probabilities and expectations of simple random processes.

Who this course is for:

This is an introductory course in Mathematics oriented toward Computer Science

Fundamental Concepts of Mathematics for Computer Science

What you'll learn

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Course content

Lecture 1 through 66 lectures • 30min

Lectures 7 through 106 lectures • 1hr 22min

Requirements

Description

Who this course is for: