Tag: math

The Only Math Resources You Need in 2022

You’d might agree that by far math can be one of the most interesting yet complex topics you can study.

You can study even the most complex concepts, but without a solid base of fundamentals things can easily fall apart. Using your college professor as a guide to consistently get better is a plus and it’s no secret that that Google offers a myriad of math resources.

Sometimes when all you’re trying to find is a step by step solution to one problem- a Google search that takes seconds could turn into an hour.

That’s why having a list of the best math resources in 2022 can save you time, and most importantly your sanity throughout this year.

We’ve taken the time to put together the best of the best in math websites in various categories. After going through the list, don’t forget to hit the bookmark icon on your browser so you can easily navigate back when you have math doubts.

Best Math Courses and Tools

Skew The Script

Let’s face it- You can either dread studying math or love it. Usually you’ll hear this from the students that’d rather skip class, “I’ll never use this in the future”.

But Skew The Script makes math relevant for everyday life and entertaining. Whether you’re interested in sports, politics, social causes, science and more;

Skew The Script has lessons that make learning math engaging and fun. With themed video explanations, student worksheets, and even teacher lesson plans, you’ll never find a dull piece of content.

Brilliant.org

From pre-algebra to more advanced topics in computer science, Brilliant.org has an expansive library of interactive courses that emphasize mastering each topic through interactive problem solving.

So if you have trouble focusing in college lectures, it would be a worthy investment checking out Brilliant’s courses made by award-winning professors from top universities like MIT and Duke.

What If Math

At one point or another you’ve probably asked yourself this:

“Why should I care about algebra? when would I ever use this in real life?”

What If Math’s main goal is to answer this question head-on. Through informative spreadsheets, What If Math applies algebra to modern-day skills that are in high demand in data science, financial literacy, computer science, and STEM problems.

Cool Math

Let’s face it, not all of us are math lovers and even learning the most fundamental concepts can be a struggle. Cool Math breaks down the most important pre-algebra, algebra, and pre-calculus topics into easily understood lessons and exercises.

For Math Enthusiasts

Quanta Magazine

Looking for some current events in the mathematics world? Or maybe you need to do research on a specific topic like why triangles are easy and tetrahedra are hard. Quant Magazine truly has it all with deep diving math articles with an enticing writing style making the content an easy daily read.

Math Values

Math Values has an enticing blog which includes articles that are meant for literally everyone to enjoy. Posts include themes like current events, politics, interviews, personal stories, and sports all tied together by math.

Math Enchantments

It’s easy to get caught up in the stress of preparing for math exams and solving textbook solutions. At times, you might be questioning why you decided to take on the challenge of a math course or majoring in it.

The Math Enchantments blog bridges the gap between creative writing and math. James Propp’s monthly posts integrates culture, math history, and storytelling keeping education and creativity as it’s main purpose.

Taking a few minutes every month to check out Propp’s short posts will give you a breather from textbook learning and a reminder of why math is fun.

Math ∩ Programming

Have you ever thought that mathematical solutions could be presented in an elegant way?

Most likely the answer was “no”. But Google engineer Jeremy Kun has creatively channeled his passion of finding mathematical solutions to programming problems through eye-grabbing imagery.

Through his intriguing writing style, don’t be surprised to be captivated for hours going into deep-diving topics.

Mathematical Gemstones

Mathematician Dr. Maria Monks Gillespie Colorado State University initially started Mathematical Gemstones to find truth in mathematical concepts. Each post is separated by hardness or “gemstones”: Amber, Pearl, Opal, Sapphire, and Diamond.

May 12, 2022
Solved: Trigonometric Identities Problem

If you’re taking a geometry or trigonometry class, you’ll most likely learn trigonometric identities.

In simple terms, trigonometric identities are equations that are related to different trigonometric functions and are true for any value of the variable. It could be hard since there are numerous trigonometry identities.

In this post you’re going to how to solve one of the top asked examples of trigonometric identities.

Solved: Trigonometric Identities Problem

Find the exact value of:

In this problem we’re asked to find the exact value of the given expression. Right away, the given expression should remind us of the sum and difference identities for sine and cosine shown below:

For our expression, notice A is equal to pi divided by 3 and B is equal to pi divided by 2. Due to the fact we have a sum, the expression is equal to the sine of the sum of the angles.

1) First, we have to find the sum of the angles and then determine the sine function value.

To add the fractions we have to find a common denominator. In this case, the least common denominator is a least common multiple of 2 and 3, which is 6. Therefore, we multiply the numerator and denominator of pi over 3 by 2, and we multiply the numerator and denominator of pi over 2 by 3:

2) Now we know:

We need to find the sine function value, which we can do using a reference triangle, or the unit circle. To use a reference triangle, we first sketch 5/6 pi radians in standard position.

The initial side is along the positive x-axis, and then we rotate 5 pi divided by 6 radians counterclockwise, which is 1/6 pi, or pi divided by 6 radians short of 1/2 a rotation, which would be approximately here. this angle here is 5 pi divided by 6 radians, and the reference angle is the angle formed with the terminal side and this negative x-axis, which is pi over 6 radians:

3) Let’s sketch the reference triangle. We should recognize this as a 30-60-90 reference triangle, where we can label the short leg 1, the hypotenuse 2, and the longer leg square root of 3.

However, we are in the second quadrant where x is negative, and therefore, the square root of 3 is negative. We can use this reference triangle to determine the sine function value, where the sine of 5 pi divided by 6 radians is equal to the ratio of the opposite side to the hypotenuse, which we can see is equal to 1 divided by 2, or 1/2. So, the exact value of the given expression is equal to 1/2.

4) Let’s also find this sine function value on the unit circle. The terminal side of 5 pi divided by 6 radians intersects the unit circle. On the unit circle, remember sine theta is equal to y, and notice how the y-coordinate is equal to 1/2.

source:Wikipedia

Conclusion

Trig identities can be overwhelming- But that’s where a high-quality textbook survival guide comes in.With it, you’ll not only be able to get the right answers, but understand concepts to prepare for the exams quickly without stress.

May 6, 2022
Applications of Integrals in Mathematics
Applications of integrals can be tricky- it can be applied to math, science, and engineering, economics etc. If you don’t have the right teacher or textbook survival guide, getting lost before exam can be easy.

In this guide you’re going to learn how integration is applied in various scenarios, the different types of integrals, and some examples.

Applications of Integrals: What does it mean?

Integrals can be applied in many different areas like math, science, and engineering, statistics,and economics.

In math, we use it to find:
- The center of mass (Centroid) of an area with curved sides
- The area between two curves
- The area under a curve
- The average value of a curve
- Integral transforms like Laplace and Fourier transforms.
When speaking about integrals, there are two different types: definite integrals (also called Riemann Integral) and indefinite integrals.

In simple terms, a definite integral has definite limits ( defined upper and lower limits/bounds) which can be represented by:

In contrast to definite integrals, an indefinite integral is an integral which has no limits. This can be represented by:

                                               (C is the constant of integration)

Solved: Example Problem of Applications of Integrals

The given function is a type of parabola, the graph is as shown below:

First, take a look at our notes below:

We will integrate the given function to get . We know that using which we will compute the value of the constant of integration. Once we know the value of constant of integration, the next step is to find f(4).

1) Knowing all that, let’s integrate .To do that, we need to apply the power rule of integration which would be:

2) Using the power rule,

                                                  ……………(1)

Thus we got the result of integration.

3) Now we will find the value of the constant of integration,

We know that , hence applying this value to equation(1) we get











Therefore we found the value of the constant of integration which is

(4) Now we will apply this value of integration constant to

Conclusion

This is just one example of many different scenarios. We have to remember in math alone there are numerous applications and in physics even more! Applications of integrals is a topic that takes practice with the right survival guides and experts to help you with solutions– you’ll be on the right track.
April 20, 2022
How to Find the Equation in Point Slope Form

Written by: Miguel Santiago (The Vegan Math Guy)

You might’ve had this experience some of my students have:

You found It REALLY hard to find the equation in point slope form in algebra class.

No matter how many hours they’d flip through their notes, they couldn’t get to the answer. In short, the next best bet is getting really effective algebra textbook survival guides and an amazing tutor (I’m a little biased :).

All jokes aside- No matter if you’re in high school or college algebra, finding the slope of a line is possible if you explain it as it is: easy.

In this post you’re going to learn what point slope form is, the equation of a line and a slope, and two examples to illustrate just how it can be.

What is point slope form?

Let’s discuss what point slope form (also called point-gradient form) is and in what situation we use it.

Simply put, it’s used to find the equation of a straight line. It’s really useful because all you need is the slope of the line and a point to find the equation.

The Equation of a Line

When you find the equation of a straight line, this is the form you can put it in:

y−y1=m(x−x1)

In the equation you can see the variables x and y. There’s also x1 and y1 which represent the point of a line on the x and y axis. Lastly we have the m value which shows the slope of the line.

So if we put this into a simple context, let’s take a look at this coordinate plane:

Imagine there’s a line that passes through the point (1,3) with a slope of -⅕ which is represented by the vertical blue line (-1) and horizontal one (5). Hypothetically, that’s how it would be expressed on a coordinate plane. Putting it in point slope form, it would like this:

y−3=-⅕(x−1)

Step by Step Examples: Find the equation in point slope form

I’m going to show you two typical examples of how to find the equation in point slope form. Check out the video below to see them step by step and read below it to see it in written form:

Let’s take a look at the two different scenarios:

Example Problem #1 : Using point slope form, find the equation of the line with slope m=⅓ and passing through (2,-1).

This is most likely the easiest scenario that you’re going to see in a point slope question. Given that we know point slope form is y−y1=m(x−x1), we need two things to solve this: the point that a line passes through and the slope:

1)Right away we know two key things:

(x1, y1)= (2,-1) and m=⅓.

2)Plug in those key values into the point slope equation y−y1=m(x−x1):

y-(-1)=⅓(x-2)

3)Simplify the left side of the equation:

y-(-1) becomes y+1

4) The final simplified point slope equation is: y+1=⅓(x-2).

Example Problem #2 : Using point slope form, find the equation of the line passing through (-5,13) and (3,-3).

In this case you can see there is no slope given but two points in which the line is passing through.

1) We know our (x1, y1). So we can choose any of the two points to plug it into the equation: (x1, y1)= (-5/13).

2)We don’t know the slope but we can plug in numbers in this equation to find it:
m=rise = y2-y1
run x2-x1

In this case the equation of a slope would look like this with the numbers plugged in:

m= (-3-13)
3-(-5)

3) Let’s simplify m= (-3-13)
3-(-5)

(-3-13)=-16=-2
3-(-5) 8

Now you have your slope (-2) and (x1, y1).

4) Lastly, let’s plug the numbers into y−y1=m(x−x1) and simply the point slope equation:

y-13=-2(x-(-5))

In this case all we need to simplify is the right side:

y-13=-2(x+5)

And that is our equation in point slope form!

Conclusion: Practice Always Makes Perfect

Understanding the core concepts of point slope form might be pretty easy. But as the old saying goes, practice makes perfect.

If you’re in a course that uses linear algebra, things can get pretty confusing fast without great study materials.

April 13, 2022