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.
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.
Rated 5 out of
5
by
Jambu from
Great Professor!
If we are not a student at the age of learning fundamentals of mathematics, for example in school grades below tenth class, we would normally think we know all about fundamentals of mathematics. Of course that would be true about addition, subtraction, multiplication and to some extent division.
But beyond that, Professor Sellers has generated such an interest in mathematics, that I have now joined a college course to learn mathematics. That much he inspired me with his classes on decimals, fractions, percentages, square roots, number theory, prime numbers, LCDs and GCFs, divisibility tricks, exponents, negative integers, geometric basics, statistics etc.
Probability session was of course difficult for me, but again that is a single introductory class, so no qualms there. I will catch up separately.
Now I am ready to start Algebra 1 by the same professor, which will be before I start my College classes in Jan 2025.
On a side/different note:
I think math is taught differently in the United States compared to how it is taught in India, in some cases. I saw specifically two such areas in this course:
1. finding the LCD has a very simple and straightforward way
2. Similarly finding a square root has a very simple way
These two topics as taught in this course is in my opinion are different/harder from the simpler ways I was taught in school in India. But this is not a complaint, just bringing up the contrasts.
All in all a great course. I enjoyed the entire course, did all the exercises in the book, and finally I love the real world examples the professor brings up to explain difficult concepts.
And of course the pizza, sprinkled all over :)
Date published: 2024-11-19
Rated 5 out of
5
by
DaGeek from
Not sure why I took this course, but…
Where was this teacher when I was in high school? When I graduated high school I felt I had no real competence in math, in fact I had a bit of a math phobia.
I started out college as a history major (not a lot of math there), but became interested in the sciences and switched to a biology major. Obviously, math was to become more important in my life. The clincher for me was my first chemistry course which, of course, required a lot of math, mainly the algebraic manipulation of formulas. I discovered I actually enjoyed it and was good at it. I went on to have a career in science related fields, then later switch to information technology as the money was better. Both fields required a fair amount of math in my day to day work responsibilities.
All that to say, is that I do not know why I took this course, perhaps due the lingering math phobia. I was intrigued by the title so I watched the first class and I became hooked. The teacher has such a good style and his explanations are clear and to the point. I also thought it would be good for my retired brain as I am always looking for ways to exercise that organ.
I did discovered that I really did remembered more than I thought, and I did pick up a few things either that I had forgotten or never knew.
If you need a good remedial course on math fundamentals, look no further.
Date published: 2024-09-24
Rated 5 out of
5
by
AndyG from
An excellent summary of the important fundamentals
This program of study provides an excellent summary of the fundamentals necessary to move up the learning ladder and master higher levels of mathematical education. The presenter does a fine job.
Date published: 2024-09-19
Rated 5 out of
5
by
Neil660 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
Ananeo 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
Johnny512 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
Campanile_ 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
Shari1 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
Overview
About
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.
Trailer
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
