Mastering the Fundamentals of Mathematics

Rated 5 out of 5 by from Simply Incredible I struggled with math my entire life, paid tons of money to tutors, bought all kinds of math books, spent hours on YouTube. Nothing in my experience comes even close to the quality and perfection of this course. This professor makes math enjoyable, fun, and teaches in a foundational way which allows the learner to build knowledge from the foundation up. Each lesson builds on all of the lessons prior to it. This kind of sequential "pyramid" type learning where each layer of knowledge is built on the preceding foundational layers, is the essence and key to learning anything. This course is perfect for the mathematically impaired, and those like me, who were on the verge of having a nervous breakdown because of a math test. I can't recommend this course strongly enough, 100 out of 5 stars. I am speechless. If you struggle with math, you owe it to yourself to go through this course. Don't waste any more time with any other course, I've tried them all, and this course beats all of them.
Date published: 2020-09-18
Rated 5 out of 5 by from Great intro pure perfection, loved his methods of teaching and keeping things organized.
Date published: 2020-09-04
Rated 5 out of 5 by from Great Teacher James A. Sellers! The lessons are simple well organized, and very clear.
Date published: 2020-09-04
Rated 5 out of 5 by from Perfect Intro Math Course This is an excellent introductory Mathematics course. It's a great refresher if you have not dealt with this type of material in some time. James Sellers is outstanding; he presents the material in a clear and concise fashion with a dash of humor. I would also recommend the workbook which has lots of problems that help you master the coursework. First rate!
Date published: 2020-09-03
Rated 5 out of 5 by from Excellent Refresher for Senior Recently, I noticed that my every-day math skills were slipping. I found this course and decided to give it a try, and I have found it to be excellent. The instructor is clear in his instructions, and the examples work well. It didn't take long, after reviewing this course, to get my math skills back. Strangely, I've enjoyed learning the math facts now, more now than I did when I was in school. Excellent course.
Date published: 2020-08-12
Rated 5 out of 5 by from The professor uses excellent examples and analogies. He also friendly with a pleasing personality.
Date published: 2020-06-08
Rated 5 out of 5 by from I reviewed the course and thought it was exceptional. I know when I go to study it, it will be a treat for me. Thank you very much!
Date published: 2020-06-08
Rated 5 out of 5 by from Very well organized The course was a great remedial review of the basic mathematical operations that one may have forgotten. The lecturer is concise and well prepared. The examples of the topics are well chosen.
Date published: 2020-05-12
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Mastering the Fundamentals of Mathematics
Course Trailer
Addition and Subtraction
1: Addition and Subtraction

This introductory lecture starts with Professor Sellers' overview of the general topics and themes you'll encounter throughout the course. Then, plunge into an engaging review of the addition and subtraction of whole numbers, complete with several helpful tips designed to help you approach these types of problems with more confidence....

33 min
2: Multiplication

Continue your quick review of basic mathematical operations, this time with a focus on the multiplication of whole numbers. In addition to uncovering the relationship between addition and multiplication, you'll get plenty of opportunities to strengthen your ability to multiply two 2-digit numbers, two 3-digit numbers, and more....

31 min
Long Division
3: Long Division

Turn now to the opposite of multiplication: division. Learn how to properly set up a long division problem, how to check your answers to make sure they're correct, how to handle zeroes when they appear in a problem, and what to do when a long division problem ends with a remainder....

31 min
Introduction to Fractions
4: Introduction to Fractions

Mathematics is also filled with "parts" of whole numbers, or fractions. In the first of several lectures on fractions, define key terms and focus on powerful techniques for determining if fractions are equivalent, finding out which of two fractions is larger, and reducing fractions to their lowest terms....

32 min
Adding and Subtracting Fractions
5: Adding and Subtracting Fractions

Fractions with the same denominator. Fractions with different denominators. Mixed numbers. Here, learn ways to add and subtract them all (and sometimes even in the same problem) and get tips for reducing your answers to their lowest terms. Math with fractions, you'll discover, doesn't have to be intimidating-it can even be fun!...

32 min
Multiplying Fractions
6: Multiplying Fractions

Continue having fun with fractions, this time by mastering how to multiply them and reduce your answer to its lowest term. Professor Sellers shows you how to approach and solve multiplication problems involving fractions (with both similar and different denominators), fractions and whole numbers, and fractions and mixed numbers....

30 min
Dividing Fractions
7: Dividing Fractions

Professor Sellers walks you step-by-step through the process for speedily solving division problems involving fractions in this lecture filled with helpful practice problems. You'll also learn how to better handle calculations involving different notations, fractions, and whole numbers, and even word problems involving the division of fractions....

32 min
Adding and Subtracting Decimals
8: Adding and Subtracting Decimals

What's 29.42 + 84.67? Or 643 + 82.987? What about 25.7 - 10.483? Problems like these are the focus of this helpful lecture on adding and subtracting decimals. One tip for making these sorts of calculations easier: making sure your decimal points are all lined up vertically....

30 min
Multiplying and Dividing Decimals
9: Multiplying and Dividing Decimals

Investigate the best ways to multiply and divide decimal numbers. You'll get insights into when and when not to ignore the decimal point in your calculations, how to check your answer to ensure that your result has the correct number of decimal places, and how to express remainders in decimals....

32 min
Fractions, Decimals, and Percents
10: Fractions, Decimals, and Percents

Take a closer look at converting between percents, decimals, and fractions-an area of basic mathematics that many people have a hard time with. After learning the techniques in this lecture and using them on numerous practice problems, you'll be surprised at how easy this type of conversion is to master....

32 min
Percent Problems
11: Percent Problems

Use the skills you developed in the last lecture to better approach and solve different kinds of percentage problems you'd most likely encounter in your everyday life. Among these everyday scenarios: calculating the tip at a restaurant and determining how much money you're saving on a store's discount....

31 min
Ratios and Proportions
12: Ratios and Proportions

How do ratios and proportions work? How can you figure out if a particular problem is merely just a ratio or proportion problem in disguise? What are some pitfalls to watch out for? And how can a better understanding of these subjects help save you money? Find out here....

30 min
Exponents and Order of Operations
13: Exponents and Order of Operations

Explore a fifth fundamental mathematical operation: exponentiation. First, take a step-by-step look at the order of operations for handling longer calculations that involve multiple tasks-complete with invaluable tips to help you handle them with ease. Then, see where exponentiation fits in this larger process....

31 min
Negative and Positive Integers
14: Negative and Positive Integers

Improve your confidence in dealing with negative numbers. You'll learn to use the number line to help visualize these numbers; discover how to rewrite subtraction problems involving negative numbers as addition problems to make them easier; examine the rules involved in multiplying and dividing with them; and much more....

32 min
Introduction to Square Roots
15: Introduction to Square Roots

In this lecture, finally make sense of square roots. Professor Sellers offers examples to help you sidestep issues many students express frustration with, shows you how to simplify radical expressions involving addition and subtraction, and reveals how to find the approximate value of a square root without using a calculator....

31 min
Negative and Fractional Powers
16: Negative and Fractional Powers

What happens when you have to raise numbers to a fraction of a power? How about when you have to deal with negative exponents? Or negative fractional exponents? No need to worry -Professor Sellers guides you through this tricky mathematical territory, arming you with invaluable techniques for approaching these scenarios....

31 min
Graphing in the Coordinate Plane
17: Graphing in the Coordinate Plane

Grab some graph paper and learn how to graph objects in the coordinate (or xy) plane. You'll find out how to plot points, how to determine which quadrant they go in, how to sketch the graph of a line, how to determine a line's slope, and more....

30 min
Geometry-Triangles and Quadrilaterals
18: Geometry-Triangles and Quadrilaterals

Continue exploring the visual side of mathematics with this look at the basics of two-dimensional geometry. Among the topics you'll focus on here are the various types of triangles (including scalene and obtuse triangles) and quadrilaterals (such as rectangles and squares), as well as methods for measuring angles, area, and perimeter....

31 min
Geometry-Polygons and Circles
19: Geometry-Polygons and Circles

Gain a greater appreciation for the interaction between arithmetic and geometry. First, learn how to recognize and approach large polygons, including hexagons and decagons. Then, explore the various concepts behind circles (such as radius, diameter, and the always intriguing pi), as well as methods for calculating their circumference, area, and perimeter....

32 min
Number Theory-Prime Numbers and Divisors
20: Number Theory-Prime Numbers and Divisors

Shift gears and demystify number theory, which takes as its focus the study of the properties of whole numbers. Concepts that Professor Sellers discusses and teaches you how to engage with in this insightful lecture include divisors, prime numbers, prime factorizations, greatest common divisors, and factor trees....

31 min
Number Theory-Divisibility Tricks
21: Number Theory-Divisibility Tricks

In this second lecture on the world of number theory, take a closer look at the relationships between even and odd numbers, as well as the rules of divisibility for particular numbers. By the end, you'll be surprised that something as intimidating as number theory could be made so accessible....

32 min
Introduction to Statistics
22: Introduction to Statistics

Get a solid introduction to statistics, one of the most useful areas of mathematics. Here, you'll focus on the four basic "measurements" statisticians use when gleaning meaning from data: mean, media, mode, and range. Also, see these concepts at work in everyday scenarios in which statistics plays a key role....

32 min
Introduction to Probability
23: Introduction to Probability

Learn more about probability, a cousin of statistics and another mathematical field that helps us make sense of the seemingly unexplainable nature of the world. You'll consider basic questions and concepts from probability, drawing on the knowledge and skills of the fundamentals of mathematics you acquired in earlier lectures....

32 min
Introduction to Algebra
24: Introduction to Algebra

Professor Sellers reviews the importance of math in daily life and previews the next logical step in your studies: Algebra I (which involves variables). Whether you're planning to take more Great Courses in mathematics or simply looking to sharpen your mind, you'll be sent off with new levels of confidence....

31 min
James A. Sellers

If you are shaky on basic math facts, algebra will be harder for you than it needs to be. Spend every day reviewing flashcards of math facts, and you will be surprised at how much better at math you are!


The Pennsylvania State University


The Pennsylvania State University

About James A. Sellers

Dr. James A. Sellers is Professor of Mathematics and Director of Undergraduate Mathematics at The Pennsylvania State University. He earned his B.S. in Mathematics from The University of Texas at San Antonio and his Ph.D. in Mathematics from Penn State. In the past few years, Professor Sellers has received the Teresa Cohen Mathematics Service Award from the Penn State Department of Mathematics and the Mathematical Association of America Allegheny Mountain Section Mentoring Award. More than 60 of Professor Sellers's research articles on partitions and related topics have been published in a wide variety of peer-reviewed journals. In 2008, he was a visiting scholar at the Isaac Newton Institute at the University of Cambridge. Professor Sellers has enjoyed many interactions at the high school and middle school levels. He has served as an instructor of middle-school students in the TexPREP program in San Antonio, Texas. He has also worked with Saxon Publishers on revisions to a number of its high-school textbooks. As a home educator and father of five, he has spoken to various home education organizations about mathematics curricula and teaching issues.

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