Search results “Algebra 1 foundations”

This math video tutorial provides a basic overview of concepts covered in a typical high school algebra 1 & 2 course or a college algebra course. This video contains plenty of lessons, notes, examples, and practice problems for you to get a good foundation in algebra.
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Here is a list of topics:
1. Introduction to Algebra - Online Crash Course Review
2. Monomials, Binomials, and Trinomials
3. Adding and Subtracting Polynomials with Like Terms
4. Multiplying Two Binomials - Foiling / Foil Method
5. Monomial & Trinomial Multiplication - The Distributive Property
6. Adding, Subtracting and Multiplying Exponents - Rules of Algebra
7. Negative Exponents - Variables and Expressions
8. Simplifying Expressions and Dividing Fractions with Variables
9. Solving Linear Equations With Parenthesis, Fractions, and Decimals
10. Simplifying Complex Fractions
11. How To Solve Quadratic Equations By Factoring
12. Solving Quadratic Equations Using The Quadratic Formula
13. Factoring Trinomials With Leading Coefficient 1
14. How To Factor By Grouping
15. Factoring Polynomials
16. Factoring Binomials Using Difference of Squares Methods
17. Factoring the GCF - Greatest Common Factor
18. Solving Equations With Variables on Both Sides
19. Solving Multi Step Equations
20. Graphing Linear Equations
21. Slope Intercept Form, Point Slope Form and Standard Form
22. How To Write The Equation of the Line
23. Parallel and Perpendicular Lines

Views: 820342
The Organic Chemistry Tutor

This algebra 1 video tutorial online course provides a nice review for those in high school or those taking college algebra. Whether you’re taking algebra lessons for 8th, 9th, 10th grade, or just studying for the EOC or common core regents final exam, this video is for you. It contains plenty of notes, formulas, examples, and practice problems that you can learn from. It is presented in a style of a lecture and it provides a nice introduction / basic overview to algebra 1.
Algebra Online Course:
https://www.udemy.com/algebracourse7245/learn/v4/content
Algebra Video Playlist:
https://www.youtube.com/watch?v=i6sbjtJjJ-A&list=PL0o_zxa4K1BWKL_6lYRmEaXY6OgZWGE8G&index=1&t=13129s
Access to Premium Videos:
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Here is a list of topics:
1. Basic Arithmetic Operation – Addition, Subtraction, Multiplication, and Division
2. How to Add, Subtract, Multiply, or Divide Two or Three Fractions
3. How to Convert Fractions Into Decimals & Simplifying Complex Fractions
4. Properties of Numbers and Negative Exponents
5. Solving One Step, Two Step, and Multi Step Linear Equations
6. Graphing Linear and Quadratic Equations
7. Slope Intercept Form, Standard Form, and Point Slope Form
8. Parallel and Perpendicular Lines – Writing the Equation of the Line
9. Order of Operations – PEMDAS
10. Solving Systems of Equations – Substitution and Elimination Method
11. How To Factor Binomials and Polynomials
12. Factoring Trinomials with Leading Coefficient of 1 and not 1
13. Natural and Whole Numbers, Integers, Real, Imaginary, Rational and Irrational Numbers
14. Solving Linear Inequalities and Absolute Value Equations
15. Simplifying Rational and Radical Expressions
16. Square Roots and Cube Root Operations
17. Fractional Exponents and Radical Expressions
18. Adding, Subtracting, Multiplying, and Dividing Rational Expressions
19. Domain and Range – Linear, Quadratic / Parabolas, Cubic, Square Root, Radicals, and Rational Functions
20. Vertical Line Test – Relations and Functions
21. Solving Exponential and Logarithmic Equations
22. Expanding, Condensing, and Evaluating Logarithmic Expressions
23. Solving Equations with Multiple Variables
24. Complex Imaginary Numbers – Simplifying, Conjugates and Standard Form – a +bi
25. Parabolas and Quadratic Functions – Vertex vs Standard Form
26. Vertex Coordinate, Axis of Symmetry, Minimum / Maximum, Domain and Range, X and Y-intercepts
27. Vertex Form – Completing the Square
28. Graphing Cubic, Rational and Radical Functions Using Transformations – Horizontal Shift, Vertifical, and Reflection about X and Y axis
29. Quadratic Equation Word Problems – Maximum Profit, Maximum Height of Ball and the time it takes to hit the ground
30. Evaluating Functions Using Synthetic Division – Remainder Theorem
31. Dividing Two Polynomials – Long Division
32. Multiplying and Dividing Variable Expressions
33. Solving Quadratic Equations by Factoring and Using the Quadratic Formula
34. Vertex Formula x = -b/2a
35. Horizontal Assymptote, Vertical Assymptote, Holes, slant / Oblique Assymptote Plus Domain and Range
36. Solving Linear Equations with Fractions and Decimals
37. Cross Multiplication, Keep Change Flip, vs Multiplying Across
38. How to Convert a Decimal to a Fraction
39. f and g composite Functions
40. Factor / Factoring – Difference of Squares Method, By Grouping, and Sum of Cubes Method
41. Graphing Linear Equations and Absolute Value Functions With Transformations

Views: 197071
The Organic Chemistry Tutor

This college algebra introduction / study guide review video tutorial provides a basic overview of key concepts that are needed to do well in a typical algebra course. High school students taking Algebra 1 and 2 can benefit from this video. It contains plenty of examples and practice problems.
Trigonometry:
https://www.youtube.com/watch?v=g8VCHoSk5_o
Epic Music Mix:
https://www.youtube.com/watch?v=qeljbZhx9bY
Algebra Online Course:
https://www.udemy.com/algebracourse7245/learn/v4/content
Algebra Video Playlist:
https://www.youtube.com/watch?v=i6sbjtJjJ-A&list=PL0o_zxa4K1BWKL_6lYRmEaXY6OgZWGE8G&index=1&t=13129s
Access to Premium Videos:
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Here is a list of topics:
1. Properties of Exponents - Multiplication and Division Rules
2. Negative Exponents
3. Adding and Subtracting Polynomial Expressions such as binomials and trinomials
4. Foil Method - Multiplying Two Binomials
5. Solving Linear Equations
6. Solving Absolute Value Equations and Inequalities
7. Graphing Inequalities on a Number Line Using Interval Notation
8. Graphing Linear Equations In Slope Intercept Form and In Standard Form
9. Identifying the Slope and Y-intercept in a linear equation
10. Graphing Absolute Value Equations Using Transformations
11. Graphing Quadratic Functions Using Transformation - Horizontal & Vertical Shift with Reflection over X - axis
12. Solving Quadratic Equations By Factoring
13. Factoring Quadratic Expressions - Difference of Perfect Squares Method
14. Factoring trinomials with a leading coefficient of 1
15. How to factor a trinomial when the leading coefficient is not 1
16. Factoring Polynomials By Grouping
17. Solving Quadratic Equations Using the Quadratic Formula
18. Factoring Quadratic Expressions with the Quadratic Formula
19. Complex Imaginary Numbers
20. Simplifying Radical Expressions With Complex Numbers
21. Composition of Functions
22. Inverse Functions & Graphs
23. Evaluating Functions Using Synthetic Division
24. Solving Systems of Equations Using Elimination and Substitution

Views: 289738
The Organic Chemistry Tutor

Why the abstraction of mathematics is so fundamental
Watch the next lesson: https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview_hist_alg/v/descartes-and-cartesian-coordinates?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Missed the previous lesson?
https://www.khanacademy.org/math/algebra/introduction-to-algebra/overview_hist_alg/v/abstract-ness?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraI
Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything.
For free. For everyone. Forever. #YouCanLearnAnything
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Views: 3545316
Khan Academy

Watch the next lesson: https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction/v/difference-between-equations-and-functions?utm_source=YT&utm_medium=Desc&utm_campaign=AlgebraII
Missed the previous lesson?
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Algebra II on Khan Academy: Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra II channel:
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Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 1820774
Khan Academy

U1F2 Day 1- Foundations of Algebra

Views: 190
Beast Algebra

The definition of cardinality is given and the method for proving that two sets have the same cardinality is provided, along with examples.

Views: 10969
learnifyable

This video reveals the unfortunate truth about the "Fundamental Theorem of Algebra": namely that it is not actually correct. This is meant to be a core result in undergrad mathematics, but curiously undergrads don't see much in the way of proof. Why? Because none of the many current arguments are actually convincing once one stops and looks carefully at them.
Modern mathematics students: prepare for some disruption to your thinking! Modern mathematicians: is it not time to admit the harsh reality? This entire topic is intimately connected with what I consider the fundamental problem in mathematics, which I discuss in the Famous Math Problems 19 lectures. And so we need some seriously new thinking.
We need to peel back the layers of conformity, imprecise thinking and wishful dreaming that characterize so much of modern pure mathematics. Help support this channel by becoming a patron, at https://www.patreon.com/njwildberger. Even just $1 per video will let you share the excitement of building up a new and better mathematics for the coming millennium. And happy new year!

Views: 7048
njwildberger

Index:
Module 1 (17:00)
Module 2 (54:45)
Module 3 (1:13:05)
Module 4 (1:26:00)
Module 5 (1:38:18)
Secondary Index (by manipulative):
Intro to Manipulatives/What’s In the Kit 12:26
Base Ten Blocks/Factor Track 17:06
Fraction Towers/Fraction Number Lines 25:45
Place Value Chips 50:50
Area Model of Multiplication (Base Ten and Algeblocks) 55:00
Cuisenaire Rods 1:13:22
XY Coordinate Board with Slope 1:20:21
AngLegs 1:22:38
Algeblocks (Expressions/Equations) 1:26:10
XY Coordinate Board (Coordinate Plane/4 Quadrants ) 1:33:30
XY Coordinate Board (Functions) 1:38:18
Teaching Foundations of Algebra?
Find FREE resources on www.hand2mind.com! Review our recorded webinar that breaks down each Module and shows how to use manipulatives to help build concrete understanding of mathematical concepts. Currently only the preliminary version is available for viewing, but check back soon for the edited searchable webinar!
For more Foundations of Algebra resources, including Small Group Manipulative Kits, contact Carolyn Cutts at [email protected]

Views: 943
hand2mind

Here we give restatements of the Fundamental theorems of Algebra (I) and (II) that we critiqued in our last video, so that they are now at least meaningful and correct statements, at least to the best of our knowledge. The key is to abstain from any prior assumptions about our understanding of continuity and "real " or "complex" numbers, and state everything in terms of rational numbers. For this we briefly first review some rational complex arithmetic, crucially the concept of quadrance of a complex number which ought to be a core definition in undergraduate courses.
These restatements were first proposed some years ago in my AlgTop series of videos. It should be emphasized that we do NOT currently have proofs for these "theorems", so there is a huge opportunity here for people to make a significant contribution to mathematics. But new and deeper understanding is required, at least I believe so, and hopefully we can aspire to computationally oriented proofs, that actually tell us how to go about finding approximate zeroes to a prescribed level of accuracy.
Working this out satisfactorily will be as significant an accomplishment as any 20th century mathematical achievement.

Views: 9035
njwildberger

We continue discussing George Boole's original algebra which can be framed as arithmetic over the bifield B_2={0,1} and vector spaces/algebra over it. We have seen how to reformulate Aristotle's syllogistic construction in terms of Boole's algebra, and use simple algebra to prove his syllogisms.
The situation is somewhat more complicated for third figure syllogisms, such as Darapti, for which "existential import" is required. This is dealing with statements about situations for which there are no instances---i.e. talking about mermaids, leprechauns, unicorms, or infinite sets :).
Then we finish the lecture by introducing the subtle, but important, distinction between the Algebra of Boole which we have been studying, and so-called Boolean algebra, which is currently used in circuit analysis, and connects more directly to set theory.

Views: 1610
njwildberger

How do we set up abstract algebra? In other words, how do we define basic algebraic objects such as groups, rings, fields, vector spaces, algebras, lattices, modules, Lie algebras, hypergroups etc etc??
This is a hugely important question, and not an easy one to answer. In this video we start by giving a bird's eye view of some basic examples, namely the first four kinds of objects on this list.
We will not attempt complete definitions, but just rather provide intuitive example based descriptions, using the standard thinking current in mathematics these days. In some videos, we will be looking to reorganize our understanding of all of these topics by being much more precise and careful, and utilizing our knowledge of data structures.

Views: 13368
njwildberger

We begin to introduce the Algebra of Boole, starting with the bifield of two elements, namely {0,1}, and using that to build the algebra of n-tuples, which is a linear space over the bifield with an additional multiplicative structure.
This important abstract development played a key role in the application of logic to circuit and logic gate analysis. Surprisingly it is not quite the same as Boolean algebra, which is closer to the arithmetic of sets. We will move towards understanding the critical difference between these two mathematical approaches to logic.
However in both cases, the situation is that mathematics was introduced to make logic more precise and rigorous---- not the other way around! This understanding has major ramifications for an appreciation of why 20th century mathematics got things so fundamentally wrong!

Views: 4292
njwildberger

There are three main branches of mathematics: arithmetic, geometry and algebra. This is the correct order, both in terms of importance and of historical development. Here we introduce our program for setting out foundations of algebra.
This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.
A screenshot PDF which includes MathFoundations46 to 79 can be found at my WildEgg website here: http://www.wildegg.com/store/p101/product-Math-Foundations-screenshot-pdf

Views: 6945
njwildberger

We investigate further the Algebra of Boole, consisting of vectors of 0 and 1 of a given size, with operations pointwise mod 2. The idempotent law x^2=x of Boole is distinguished. To illustrate the geometry, we look at a 5 dimensional example and the span of three vectors, along with the algebra generated by them, giving both a 3 dimensional cube and a 4 dimensional hypercube.
Then we introduce the square of opposition going back to medieval philosophers, now in algebraic form by re-interpreting Aristotle's propositions using Boole's algebraic reformulation. Then armed with this mathematical framework, we begin the fun task of proving Aristotle's syllogistic rules using just mathematics! Including Barbara, Celarent, Cesare and others.

Views: 2360
njwildberger

This Fort Bend Tutoring [fbt] Live Stream is part 1 of 2 final exam review videos for the developmental mathematics college course foundations of mathematics (Developmental Mathematics II). Math concepts, from the course MATH 0308/MATH 0409/MATH 0309, covered are solving linear equations, factoring quadratic equations and graphing linear equations. Feel free to participate, ask questions and donate using the Super Chat feature on a laptop or desktop or the link below. Instruction by Larry "Mr. Whitt" Whittington.
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Purchase our Simply Math Workbook #2 for more examples and over 200 practice problems!
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Views: 4512
Fort Bend Tutoring

This video gives an overview of Algebra and introduces the concepts of unknown values and variables. It also explains that multiplication is implicit in Algebra.
The first video in the Algebra Basics Series:
https://www.youtube.com/watch?v=NybHckSEQBI&list=PLUPEBWbAHUszT_GebJK23JHdd_Bss1N-G
Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!

Views: 1835573
mathantics

Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science. This mini-course covers these areas, providing intuition and rigorous proofs. Connections between Geometry and Probability will be brought out. Text Book: Foundations of Data Science.
See more on this video at https://www.microsoft.com/en-us/research/video/foundations-of-data-science-lecture-1/

Views: 9247
Microsoft Research

The simplest and most common examples of abstract algebraic objects are probably linear spaces. They occur in many areas of mathematics, and are pillars of linear algebra, where they are often called vector spaces. Our approach will be to generalize simple aspects of Nat, Int and Rat from a data structure orientation, prominently using multisets, or msets.
In this lecture we start with the idea of generalizing Nat with addition, to form spans of msets.

Views: 3713
njwildberger

The first of a series that will discuss foundations of mathematics. Contains a general introduction to the series, and then the beginnings of arithmetic with natural numbers. This series will methodically develop a lot of basic mathematics, starting with arithmetic, then geometry, then algebra, then analysis (calculus) and will also treat so called set theory.
It will have a lot of critical things to say once we get around to facing squarely up to the many logical weaknesses of modern pure mathematics.
The series is meant to be viewed sequentially. We spend a lot more time and effort than usual on fundamental issues with number systems. If you are a more advanced student, or a fellow mathematician, then the first few dozen videos might be a bit slow. But they are none-the-less important!
Screenshot PDFs from my videos can be found at http://wildegg.com. These give you a concise overview of the contents of each lecture.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h .
A screenshot PDF which includes MathFoundations1 to 45 can be found at my WildEgg website here: http://www.wildegg.com/store/p100/product-Math-Foundations-A-screenshot-pdf

Views: 102490
njwildberger

Roots of unity as regularly spaced points on the unit circle in the complex plane are common-place objects in algebra, but they implicitly rely on the Fundamental theorem of algebra for their existence. But their existence, in fact their definition, is fraught with logical difficulty, at least when we view them in the complex plane.
In this video we summarize some basic algebraic and geometrical properties of complex numbers, centered on the rational parametrization of the unit circle. There is a huge difference between specifying a unit quadrance complex number by an expression like 3/5+4i/5 and cos 4+i sin 4. Once we understand that, we can start to appreciate the logical difficulty in supposing that something like the seventh roots of unity really do exist, perfectly spaced around a regular septagon.

Views: 8852
njwildberger

Georgia High School Graduation Test Content:
http://www.stephenwelchtutoring.com/GHSGT.html

Views: 407
Stephen Welch Tutoring

After George Boole's introduction of an algebraic approach to logic, the subject morphed towards a more set theoretic formulation, with so called Boolean algebra initiated by John Venn and Charles Peirce. Venn diagrams (originally going back to Euler), give us a visual way of representing relations between subsets of a universal set. The operations of meet and join, or intersection and union, together with taking complements become replacements for the product and sum of the Algebra of Boole.
In this set theoretic context, de Morgan's laws clarify how to compute complements of unions and intersections, and the two distributive laws involve 3 sets, and either a union of an intersection, or the intersection of a union. We illustrate how to verify these laws from, first of all a truth table perspective, and then with computations using the Algebra of Boole.
There is a heretical message here: professors teaching circuit analysis to engineers might want to start thinking about revamping their subject, and replacing Boolean algebra with the original, more powerful and simpler Algebra of Boole!

Views: 1557
njwildberger

There is a very big jump in going from finite algebraic objects to "infinite algebraic objects". For example, there is a huge difference, if one is interested in very precise definitions, between the concept of a finite group and the concept of an "infinite group".
We illustrate this important distinction in this video by looking at a rich and interesting example: SL(2) with just 0,1 entries mod 2, which is a lovely and special finite group, and SL(2) with arbitrary integer entries, which is also an interesting and important mathematical object, but which ought to be defined and treated differently.
Of course one of the advantages in the modern sloppy approach to the definition of a "set" is that it does not distinguish at all between a collection that can be explicitly listed and one that cannot be. So this meaningful distinction can be left under the carpet.

Views: 3213
njwildberger

Yay Math in Studio returns, with the help of baby daughter, to share some knowledge about parent functions and their transformations. Specifically, we use the absolute value graph as an example to demonstrate horizontal shift, vertical shift, reflection, and stretch. Transform your graphing, and your life, along with me. YAY MATH!
For all videos, free worksheets and quizzes, books, and entire courses you can download, please visit yaymath.org
Please visit http://www.yaymath.org for:
all videos
free quizzes
free worksheets
debut book on how to connect with and inspire students
entire courses you can download
Music attribution:
Mandeville by Kevin MacLeod is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100809
Artist: http://incompetech.com/

Views: 74663
yaymath

The definition of a group is given, along with several examples.

Views: 45898
learnifyable

Learn More at mathantics.com
Visit http://www.mathantics.com for more Free math videos and additional subscription based content!

Views: 611993
mathantics

Matrix theory is just a shadow of the more fundamental and far-reaching maxel theory. In our last video we introduced maxels from integers, which gives us a broad canvas to restructure matrix theory, extending to integer indices. In this video we begin to discuss the ramifications of this larger two-dimensional view of linear algebra.
We review some constructs from earlier videos, and extend them to this more general set up, such as the partial identity maxels e_J corresponding to a set J of integers that allow us to identify matrix subalgebras inside our maxels.
A lovely feature of this view is that a fundamental shift invariance comes into focus, which is not available in the more classical matrix view. The entire integer screen supporting maxel theory has a symmetry which allows us to shift up or down along the main diagonal.
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.
A screenshot PDF which includes MathFoundations184 to 212 can be found at my WildEgg website here: http://www.wildegg.com/store/p105/product-Math-Foundations-C2-screenshots-pdf

Views: 1630
njwildberger

This video tutorial provides a review on how to find the domain and range of a function using a graph and how to write or express it using interval notation. This video is for those who may be taking algebra 1 or 2, trigonometry, precalculus or calculus and who wants to have a solid foundation on determining the domain and range of an equation. This video contains plenty of examples and practice problems.
Algebra Online Course:
https://www.udemy.com/algebracourse7245/learn/v4/content
Precalculus Video Playlist:
https://www.youtube.com/watch?v=0oF09ATZyvE&t=1s&list=PL0o_zxa4K1BXUHcQIvKx0Y5KdWIw18suz&index=1
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
1. Domain and Range of a Graph – Closed and Open Circles – Parentheses vs Brackets
2. Piecewise Function / Graph – Continuous and Discontinuous Functions
3. Writing the Domain and Range Using Interval Notation
4. Horizontal and Vertical Assymptotes Including Holes
5. Linear Functions and Equations – Slope Intercept Form
6. Domain and Range of Quadratic Functions / Equations and Parabolas
7. Domain and Range of a Cubic Function
8. Polynomial Functions – Domain – All Real Numbers
9. Parent Functions and Transformations – Horizontal & Vertical Shifts Plus Reflection About X and Y Axis
10. Domain and Range of Radical Functions – Square Root and Cube Root
11. Using a Number for the domain and range of a square root function
12. Rational Functions – Fractions, Horizontal, Vertical, Slant / Oblique Assymptotes
13. Absolute Value Functions and Equations
14. Domain and Range of Exponential and Logarithmic Functions
15. Domain and Range of Trigonometric Functions
16. Trig Equations – sin cos tan
17. Domain of Sine and Cosine – All Real Numbers
18. Range of sine and cosine – Restrictions – Amplitude and Midline
19. Range of Tangent Function – All Real Numbers

Views: 145860
The Organic Chemistry Tutor

One important use of letters in algebra is to describe patterns in a quantitative and general way. We look at the `sequences' of square numbers and triangular numbers, and derive formulas for the nth terms. A table of differences shed light on these and other number patterns.
This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.
Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of each lecture. Great for review, study and summary.
A screenshot PDF which includes MathFoundations46 to 79 can be found at my WildEgg website here: http://www.wildegg.com/store/p101/product-Math-Foundations-screenshot-pdf

Views: 10254
njwildberger

Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 1: Algebra. The main topics in this section are exponent laws, polynomials, distributive property, and solving first degree equations.
Please watch part 2 and 3 for a review of linear relations and geometry.
If you watch all 3 parts, you will have reviewed all of grade 9 math in 60 minutes. Enjoy!
Visit jensenmath.ca for more videos and course materials.

Views: 175485
MrJensenMath10

This Fort Bend Tutoring [fbt] Live Stream is part 1 of 2 final exam review videos for the college level course College Algebra (College Mathematics). Math concepts, from the course MATH 1314, covered are solving exponential equations, factoring quadratic equations and graphing functions. Feel free to participate, ask questions and donate using the Super Chat feature on a laptop or desktop or the link below. Instruction by Larry "Mr. Whitt" Whittington.
Subscribe to Fort Bend Tutoring [fbt] here: https://goo.gl/JuczKk
Purchase our Simply Math Workbook #12 for more examples and over 200 practice problems!
http://shop.tutormemath.net/product/simply-math-workbook-12
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Views: 21668
Fort Bend Tutoring

In the modern European era, medieval logic is replaced with new directions, motivated by an increased interest in systematizing reasoning. A prominent thinker in this direction is G. Leibniz, who applied his genius to, among many other things, the idea of a computing device and language that might allow systematic, even mechanical reasoning. In the 18th century, Euler, Lambert and Ploucquet introduced diagrams for representing logical relations.
And then in the 19th century we move to more dramatic developments, largely due to the work of De Morgan and George Boole. We include some original work by Boole himself to get a sense of his thinking. This is when mathematics first intrudes on classical logic, presenting an algebraic approach to Aristotle's syllogisms, while both expanding the subject and restricting its interpretation to binary possibilities.

Views: 3683
njwildberger

Given two binary inputs p and q, there are four possible assignments of 0's and1's to them, and correspondingly 16 different possible connectives or operations on these four assignments. The systematic study of these 16 connectives forms the foundation for both Boole's algebra, Boolean algebra, and modern circuit analysis. We want to position these subjects so that Boole's algebra is primary.
We introduce AND, OR, XOR gate terminology, as well as the negations NOT, NAND, NOR, XNOR and also the implication operations IMP and NIMP. We illustrate the situation with a study of Modus Ponens both through truth tables and a more algebraic analysis based on Boole's algebra.
This will give us a powerful new insight that allows us to apply very elementary polynomial algebra to solving complex problems in electrical engineering.

Views: 1835
njwildberger

Algebra starts with the natural and simple problem of trying to solve an equation containing an unknown number, or `variable'. Here we start with simple examples familiar to public school students.
This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.
The idea is to transform an equation with a variable into a simpler but equivalent equation, which can be more easily solved. We review examples of such manipulations--that go back to Hindu and Arab mathematicians.
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/Norman_Wildberger. I also have a blog at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things, and you can check out my webpages at http://web.maths.unsw.edu.au/~norman/. Of course if you want to support all these bold initiatives, become a Patron of this Channel at https://www.patreon.com/njwildberger?ty=h .
A screenshot PDF which includes MathFoundations46 to 79 can be found at my WildEgg website here: http://www.wildegg.com/store/p101/product-Math-Foundations-screenshot-pdf

Views: 6291
njwildberger

We introduce some deceptively simple but important notation to deal with multisets/msets from n, for some natural number n. In particular we augment addition of msets with multiples of an mset, and use that to give a list-theoretic description of the multiplicity of various elements that appear in a given mset.
In particular this suggests the possibility of extending multiplicities to have negative, or even rational number values. Both of these ideas will have major consequences as we use data structures to help us structure parts of modern algebra.
Please consider supporting this Channel bringing you high quality mathematics lectures by becoming a Patron at https://www.patreon.com/njwildberger?
Screenshot pdf's for the lectures are available at http://www.wildegg.com/divineproportions-rationaltrig.html
My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/
A screenshot PDF which includes MathFoundations150 to 183 can be found at my WildEgg website here: http://www.wildegg.com/store/p104/product-Math-Foundations-C-screenshot-pdf

Views: 3973
njwildberger

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Pool Accessary Options. Types of Pool Water Sanitation. There are a variety of pool water treatment options beyond the traditional chlorine, although it remains the most popular option. Chlorine is added to a pool to combat algae or other bacteria that can gather in the water. Chlorinated water relies on a proper pH balance to prevent an overly chemical-smelling pool. While saline pools, also known as saltwater pools, are not chlorine-free, they consist of a salt-chlorine generator that produces lower levels of chlorine. Mineral water pools are chlorine-free and use disinfecting minerals to prevent bacteria and algae. Pool Maintenance.