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Mastering the Fundamentals of Mathematics

An award-winning professor teaches you the mechanics behind math. Refresh your skills, keep your mind sharp, and appreciate the beauty of mathematics.
Mastering the Fundamentals of Mathematics is rated 4.9 out of 5 by 126.
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Rated 5 out of 5 by from Flawless I'm a mature student doing an MA in International Relations. I've taken a year out to teach myself economics and statistics, but first need to brush up my basic maths. The tutor is flawless, as is the course- he's engaging and obviously passionate about his subject, as well as extremely knowledgeable. The pacing is perfect, the problems are numerous and there are additional question sets in the accompanying book. I'm now looking forward to taking the next maths courses by this professor, algebra 1 and 2. One thing I would like to see is a suggested curriculum pathway for the maths courses. There is a wonderful maths ecosystem on Great Courses, but it's hard to piece the areas together. For example- an Economics Pathway could suggest, 1) Mastering the Fundamentals of Maths 2) Algebra 1 3) ... ? This is where I'm not so sure. Should I study statistics first or the Algebra 2? In any case, this is just a suggest and doesn't detract from the wonderful course and the stellar teacher.
Date published: 2024-07-09
Rated 5 out of 5 by from Great intro course with a master teacher Nothing to add beside what a great course it is and what a skilful teacher.
Date published: 2024-07-03
Rated 5 out of 5 by from Awesome Instructional! Must Buy! My mathematics in school has always had holes... Something were solid but always got lost in the fractions. As a construction worker, I can read a tape measure any kind of way. Even though I didn't purchase this course just subscribed to The Great Courses on Amazon Prime, definitely buy for my own copy. Really assigns problems in every dimension, so you won't be confused, To add as a tip to his course desciption; one needs to learn the vocabulary of grammar in mathematics. Then one can study math as a language to manipulate vs learning simply steps. Must get an understanding.
Date published: 2023-12-27
Rated 5 out of 5 by from Fantastic course on arithmetic/pre-algebra! Let me say up front that this is a fantastic course, and Prof. Sellers is an excellent teacher—in fact, I'd rate him as one of the best professors TGC has to offer! For anyone interested in the topics covered, this is a strong recommend. As Prof. Sellers states in the introduction, this course is meant to include a number of topics taught in a typical school "pre-algebra" course. He definitely succeeds with that objective. All the basic topics in arithmetic and pre-algebra are covered. This means you can use this course with any standard pre-algebra/basic math textbook if you want extra problems to work on beyond what is provided in the accompanying workbook. (As an aside, one of my favorite parts was the two lectures on number theory, a subject area that is sometimes overlooked.) "Fundamentals of Mathematics" works either as a course for someone who learned the material in the past but needs a review/refresher, or as an introduction to the topic for someone learning it for the first time. I think both audiences would be well served by viewing these lectures. Also, if you know a student who is struggling with learning pre-algebra mathematics, do them a favor and give them this course because Sellers is one of the best math explainers out there. Prof. Sellers style of teaching involves explaining the concepts, and then working through a number of problems in order to ensure that the viewer understands and masters the material. The accompanying workbook also does a good job of reinforcing the concepts taught in the lectures. And, Prof. Sellers states upfront that you do not need a calculator to do this course. This course replaces an older course "Basic Math" by Murray Siegel that was published by TGC back in 1997 (it's a shame we can't have both!). By way of comparison, Basic Math covered mostly the same topics (as well as some more advanced stuff), but sometimes presenting the material with a slightly different twist.
Date published: 2023-11-24
Rated 5 out of 5 by from Great Review of Basics of Math Amazed at how much I have forgotten through the years!! So glad I have this course to refresh my math skills and excellent exercise for using my brain!! I plan to also take Algebra 1 at least. I was a good math student but had not used a higher level in years. Professor Sellers is an excellent instructor by insuring his explanations easy to follow. He doesn't intimidate the student.
Date published: 2023-10-28
Rated 5 out of 5 by from Professor Sellers is a gifted teacher. His enthusiasm for math is contagious. Thank you for a great course.
Date published: 2023-03-07
Rated 5 out of 5 by from Excellent! I signed up for Wondrium?Great Courses a couple years and do not regret the monthly pay-out. I called and ordered the workbook for this course and have worked through it when I can. I am almost finished. I am an adult and working to expand my career opportunities and am facing challenges in college. Going through this course has helped me to brush up and even learn new material that I never thought was valuable when I was a kid in school. I started this on my own last year and moved through the primary work pretty quickly but did all the work nonetheless. Now that I am back in college and facing demanding math requirements, I am back here and have almost finished this entire course. I can't wait to jump into Algebra 1 and move onto Algebra 2 and onto Trig and calculus! This will help me in my career work and I am very excited to have this at my fingertips. The cost of the workbook was very reasonable and it is very well laid out. Its like having a teacher in my house that I can call on! Yes, this takes work, yes sometimes the lectures are boring, yes I have to review and re-run the video to catch key points, but its all in how hard you work. I recommend this course for anyone who missed a lot of the learning process in math in high school or before; especially if you have anxiety -- work through at your own pace and you can even supplement the lecuture and book with references outside on Google. It all will come together. i can't say enough good about the Great Courses/Wondrium program!
Date published: 2022-10-23
Rated 4 out of 5 by from The professor and the class is wonderful This is a wonderful refresher and I intend to recommend it to friends who were over looked in their math classes and missed important bits in their schooling. My only issue is the guidebook. There are no answers to the practice exercises and there are a few large mistakes in the definitions. It needs an edit and answers.
Date published: 2022-07-22
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Whether you're a high-school student preparing for the challenges of higher math classes, an adult who needs a refresher in math to prepare for a new career, or someone who just wants to keep his or her mind active and sharp, there's no denying that a solid grasp of arithmetic and prealgebra is essential in today's world. In Professor James A. Sellers' engaging course, Mastering the Fundamentals of Mathematics, you learn all the key math topics you need to know. In 24 lectures packed with helpful examples, practice problems, and guided walkthroughs, you'll finally grasp the all-important fundamentals of math in a way that truly sticks.


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!


University of Minnesota Duluth

Dr. James A. Sellers is Professor of Mathematics at the University of Minnesota Duluth. He earned his B.S. in Mathematics from The University of Texas at San Antonio and his Ph.D. in Mathematics from Penn State. 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.

By This Professor

Mastering the Fundamentals of Mathematics
Algebra II
Algebra I
Mastering the Fundamentals of Mathematics


Addition and Subtraction

01: 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

02: 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

03: 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

04: 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

05: 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

06: 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

07: 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

08: 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

09: 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