4 important steps to learn math form the ground up

50% of the US population suffers from mathematics, some people say they want to learn math from the ground up.

is it possible to learn mathematics from the ground up?

the response is yes. But the question is how to learn math from the ground up?

in this post were going to list the 10 important that could any beginner or zero-knowledge follow to learn math from the ground up.

in addition, we will prove free resources for each math topic so you start learning math right now. So will not have more excuses anymore.

Step 1 learn algebra

We consider that you don’t know anything in math so we will begin from zero. If you know this algebra topic you could skip to the next paragraph.

learn arithmetics

The first thing that you should begin with is arithmetics that is to say control and learn the 4 famous operations:

  • addition
  • multiplication
  • subtraction
  • division

these 4 things are the pillar of math so having troubles in these pillars elements result in high problems for the future steps. Addition and subtraction are easy, but when we talk about multiplication or division some students stuck up.

The solution to this problem is you should memorize a multiplication table. If you still struggling with 7X9 or 8X8 you don’t have the right o move to the next step.

if you learn a multiplication table division will be easy for you.


The second thing that you should learn is factorization which is mean reducing and simplifying math numbers or equations. I will give one simple example in the line below.

16+8 = 2 (8+4) = 4( 4+2) = 8(2+1)

this was the simple example some students will find silly but the goal is to keep mathematics newbies close to what talk about.

to learn and perform well factorization you should have a solid background in arithmetic and have a multiplication table in the mind.


the next steep come is to learn fractions and their operations as a student you have to learn how to:

  • add fractions
  • subtract fractions
  • multiply fractions
  • divide fractions
  • reduce fractions

these 5 operations are very important and we will give an example for each operation in the image below.

it is a very basic example, so as a beginner and a student who learns for ground-up learning fractions is very important. You have to train well and make a lot of exercises in these subjects.

And you have to remember to take your time and know that math requires a lot of time. in the beginning, things are going to be hard but with time things get easier with practice and work.


equations are the tool that mathematics use to solve math problems, to simplify without any complications:

5+5= 10 is an equation

10 X 5= 50 is an equation

but if someone tells you that the school has 20 classes and each class contains 30 students. So what are the global students’ numbers in the school?

so we will use the equation to solve this math problem and our equation is :

20 X 30 = X


X is the number of students.

So as a student you need to learn equations and how to implement them to solve issues like the example we listed above.

Equations first degree

as we learn in the equation in the last paragraph now is the time that students have to learn that equations are principally 2 types:

  • first-degree equation
  • second degree equation

the first type of equation is wort like this forme


The second-degree equation degree is written like this forme below:

ax² + bx +c =0

The first type of equation is that we used in our first example exercise of students. and the second one Is what we’re going to explain in the next paragraph.

so for the first equation type, you have as a student who learns math from the ground to understand it well and to manipulate the first degree equations and solve them.

equations second degree

for the second degree equation you need to learn how to solve this type of equation the tools that you should be aware of are:

  • all basics that we listed before in the article
  • learn how to apply the rule of Δ = b² – 4ac

you will find in this video below the all details about what is second equation degree is and how to solve it.

The three rules that you should engrave in mind

(a+b)² = a² + b² + 2ab

a² + b² = (a-b)(a+b)

(a-b)² = a² + b² – 2ab

These 3 rules equations have to be engraved in the mind you should memorize them they are so helpful for a student who wants to learn math from the ground up and special for algebra.

Step 2 learn geometry

the second step after learning algebra is to learn geometry, that is to say, the math that relates to space and geometric forms.

points lines and planes

learning point and plans mean in geometry being able:

  • what is are the points in math
  • what is a segment in math
  • to differentiate between a segment and line

you will learn the first perception and explanation that math uses to interpret objects. This part you will find in this video.


the second thing that you should learn in algebra is the meaning of angles. what are angels and what do they serve for?.

in this part, you should learn how to measure the angle and discover the degree as a principal unity to measure angles. in addition, you should learn how to do some operations on angles like:

  • addition (add 2 angles)
  • subtraction (subtract 2 angles or even more)
  • multiplication
  • division

Also, you should learn the 3 types of angles who are:

  • Acute angle
  • obtuse angle
  • right angle

you will find the angle lecture in the video( part1, part2) you should take attention to it because angles are so important in geometry is the base of geometry.


triangles are very important in geometry so as a student who is learning math from the ground up you will learn what are:

  • Right-angled triangles
  • Isosceles triangle
  • equilateral triangle

These 3 triangles are the principal and basic types of triangles that a ground-up math beginner should learn about. Also, know their rules and basics.

you could watch this explicit video about traingles.

sinus and cosine

the following step after understanding about angles and triangles is learning the famous 3 functions geometry rules who are:

  • Sine
  • cosine
  • Tang

it is so important o learn these functions in geometry because they rule triangles and geometry, Also should learn some math rules and relations between them like these 2 examples:

Tang θ = Sin θ / Cos θ

CoTang θ= Cos θ / Sin θ

you could watch this video is enough to teach what is cos and sin.

there is a part 2 that you should go and check-up.


the next step in algebra is to learn vectors, you will learn what are vectors as a definition and what works for. Also doing some operations on them like:

  • addition
  • subtraction
  • multiplication
  • division

vectors are very important to use for solving a geometric equation so for math students who learn math from the ground they should not ignore them at all.

geometric theorem

There is a lot of geometric theorems to learn in math that students should learn, Pythagoras is one of the famous ones as an example there is are 3 principles of geometric theorems that you should be aware of:

  • circle theorems
  • angles theorems
  • triangles theorems

as we said Pythagoras is considered one of the triangle theorems. But as a student, you should not memorize them all unless you use them in exams when you can’t access documents.

But the important thing is to understand them and apply them in many exercises examples. you will find all the theorems courses you will need in this free course.

Step 3 calculus

The level that we’ve seen above in the 2 steps or parts was a level of elementary and middle school. So in this step, we’re going to go to an advanced level high school and college students study which is calculus.

Calculus is a nightmare for many students, calculus is one of the principal reasons that make many students drop from stem major.

for example, most math students don’t major in CS or drop in the first year.

you could read these 2 related articles:

calculus is considered one of the difficult math subjects that students suffer from. But if you follow the instructions and learn well calculus as a math subject from the ground up you won’t face problems.

calculus are 3 principal components:

  • limits
  • derivative
  • integrals


Before going ding into calculus subject you should a student who learns math from the ground up, you have to know that math functions are numerous and the principals one that you will use are:

  • polynomial function
  • linear function
  • power function
  • quadratic function
  • polynomial function
  • rational function
  • exponential function
  • logarithmic function
  • sinusoidal function

it is very important to differentiate between these functions to not fall into trouble in calculus. it is not hard just a little effort of memorization.


The first thing that you should begin to learn in calculus is limits you will learn how to make operations limits like in this example below.

you don’t have to worry there are simple you just have to take time to learn them.

as advice limits require 2 things to be strong at them:

  • memorize their rules (you will find them all in this link)
  • a lot of practice by doing a lot of exercises to be used and comfortable implementing these rules

if you follow these 2 rules you won’t struggle with limits anymore.


the second pillar in calculus is derivative which is a principal study that is similar to limits rules. In derivatives, you will learn how to derive functions and do all operations.

to summarize derivative need to apply the same 2 important rules to learn who are:

  • memoize the all derivative operations you will find in this link
  • The second thing is practicing a lot of math exercises to engrave these rules


the last part of calculus is to learn integrals But you should know one interesting thing about that.

if you didn’t understand well limits and derivatives you will suffer in integrals and this is why most students fail and hate calculus. calculus objects are very correlative so don’t rush.

integrals base a lot on derivatives, but to summarize to learn integrals you will need to use the same strategy that we mentioned in with limits and derivatives.

  • learn the basics or fundamentals of integrals you will find the in this link
  • do a lot of exercises and practice a lot to retain theses rules

step 4 probability and statistics

to learn probability and statistics I will let you with this introductory video of probability and statistics that explain the basics of them.

Khan academy is very famous so if you go on its channel you will find all you need to study for any math subject even with math and statistics.


as we’ve seen to study math from the ground up you have to follow 4 interesting steps who are:

  • studying algebra
  • knowing trigonometry
  • studying calculus
  • studying probability and statistics

But to study these heavy subjects students have to be patient and respect these 4 rules:

==> the first rule is you have to understand well the lecture before going to exercises the more you understand the lecture the more is better for you

==> the second thing is practice, math requires a lot of practice you should make dozens of exercises to absorb math subject. Because a lot of people underestimate how much work is required to learn math subject is not easy.

==> the third rule is you should ask for help, if you didn’t understand don’t waste a lot of time ask for help use internet or whatever tool to find the information.

==> the last thing is don’t skip steps. In other words, if you skip steps you will pay the price, learning math from the ground requires time. You should know that the program that you have between your hand is a summarise of 15 years of math school, from middle school to college.

Good luck.


Yassin ajanif is a physics graduate and electromechanical engineer width more than 5 years in the field. My goal and my team are to share our experience to help you succeed in your career as a stem major. we talk about all tips, problems, and struggle STEM students face in their career and how to overcome them.