In this video, I discuss the six basic trigonometric functions and their graphs. I cover transformations such as a change in period, phase shift, amplitude, and vertical and horizontal shifts. I work on five examples in detail.
Are you interested in mathematics? Whether you’re a professional mathematician or a beginning student, if you’re looking to connect with Dave, you’re in the right place. In this article, I go through each of the social media platforms on which I’m promoting mathematics. I also discuss each platform’s benefits and how I use it to educate and encourage mathematical exploration.
In this article, I discussed the 10 best Facebook pages related to mathematics. For each Facebook fan page, I run through why you should be a follower. Of course, these are pages that have tons of engagement about mathematics. So, find out what makes these pages so intriguing.
In this article, I show you the 10 best LinkedIn pages related to mathematics. For each page, I run through exactly why it made the list. First, each page must have published at least one post in the last year. Second, each of the pages is primarily involved with helping promote mathematics throughout the world. Each of these LinkedIn pages must have at least 3K followers and lots of engagements. Find out what makes these LinkedIn pages the ones to follow.
Before running through the 13 best Instagram accounts related to mathematics, I explain to you how I formed this list. First, the accounts needed to have made at least one post in the last year. Secondly, these are Instagram accounts that are primarily engaged in promoting enthusiasm for mathematics. And each one has at least 1K followers and has lots of engagement by other people. I also walk through one of the most commented post for each account.
In this article, I run through the 52 best Twitter accounts related to mathematics. For each channel, I talk about how often they tweet and their engagement with their audience. I also talked about how many followers they have and their most retweeted tweets from the past year. Find out what makes these accounts so interesting.
In this article, I talk about the 25 best YouTube channels for mathematics. For each YouTube channel, I run through what topics the channel covers, how the mathematics is presented, and where. Other statistics, such as publishing rate and video length, are also discussed. Finally, I talk about viewership and engagement for each channel.
Okay, so you understand how to check if a quadratic congruence is solvable, but how do you find the solutions? In this article, I cover the Tonelli-Shanks algorithm by working through several examples. I also give a complete solution to a general quadratic congruence equation.
There are so many applied math journals out there; how can you keep track of them all? How do they relate to each other, what types of research does each one represent? Who should use applied mathematics journals to publish their work? And how do they work? In this article, I go over these questions by listing many applied mathematics journals and going over each one.
In this article, I cover topics related to solving quadratic congruences. In particular, I explain quadratic residues and the Legendre symbol in detail.
I wrote this article for those with a beginning interest in mathematics. Here I explain some of the primary areas of mathematics by grouping them into math topics and then discussing each one. This organization is only a broad overview, though I hope it helps you find your specific area of interest.
Many people have celebrated Euler’s Theorem, but its proof is much less traveled. In this article, I discuss many properties of Euler’s Totient function and reduced residue systems. As a result, the proof of Euler’s Theorem is more accessible. I also work through several examples of using Euler’s Theorem.
Mathematics uses numbers as a language to explore some of the world’s most complex theories and problems. Children in school associate math with difficulty or confusion. With proper study, the subject can become an exciting way to view the world. Read all about the topic and its many branches.
Maybe you have heard of Wilson’s Theorem? But did you know that’s is converse also holds. In this article, I prove both Wilson’s Theorem, its converse, and Fermat’s Theorem. Then you will also see many examples using Fermat’s theorem.
In this article, I take a look at classic mathematics. I discuss intuitionism and constructivism and the uses of classical mathematics throughout time. Then, from the Islamic Golden age to European developments, I review some of its histories. I also briefly explain some of the elementary fields of classic mathematics. In the end, mathematics concerns itself with the search for truth.
This definitive guide covers proofs, examples, algorithms, applications, and the Chinese Remainder Theorem history. It also includes links to additional resources such as online articles, courses, books, and tutors to help students learn from various sources. Professionals can also use these resources to increase their knowledge of the field or help structure courses for their students.
So you probably know a divisibility test for 2, 3, and 5. But what about 7, 11, 13, or even larger primes? In this article, I go over divisibility tests. Including how to create your own. I also discuss the Days of the Week problem, where you are to determine the day of the week from a given date very quickly.
The idea behind solving polynomial congruence equations is that we can reduce a congruence equation to an equivalent system of congruence equations using prime factorization. We then 1) solve each equation modulo a prime number (by brute force), 2) use Hensel’s Lifting theorem, and then 3) piece together the solutions using the Chinese Remainder Theorem. We provide several nontrivial examples many of which are workable by hand.
In this article, you will learn what linear congruences are and when they are solvable. How to solve them will also be covered in detail. I discuss an ad hoc method, using the Euclidean algorithm, and using the inverse of an integer.
In this article, I discuss modular congruence. I demonstrate the congruence is an equivalence relation, and I prove several lemmas concerning the basic properties of congruence. Towards the end, I go over modular arithmetic and its properties.