Chances are that at this very moment you’re procrastinating on something. Maybe that’s the reason why you’re reading this article on how to overcome procrastination once and for all …
The other day I was thinking to myself about how difficult it’s become to stay focused for our current generation. I made it through my days at School and through my days at University. Not saying that they were easy, they were far from it! I still had distractions, but through understanding a bit about psychology/motivation and deliberate action, I’ve managed to minimize my bad habits and have successfully replaced them with good ones.
How have I finally overcome procrastination? How do I wake myself up early? How do I complete the hardest tasks firsts? How do I make sure that I achieve exactly what I need to do each day, week and month? Let me tell you.
There are several actions that accumulate and become habits, compounding with each other to give me and soon you the ability to overcome procrastination.
Lets Understand a couple of thing first, such as;
Procrastination is a human condition. Majority of people admit to putting off work and I would argue that the rest are lying or putting off giving an answer.
As for putting stuff off, it’s a purely visceral, emotional reaction to something we don’t want to do. The more averse you find a task, the more likely you are to procrastinate.
In his research, Tim Pychyl identifies a set of seven triggers that make a task seem more averse. Bring to mind something you’re putting off right now — you’ll probably find that task has many, if not all, of the characteristics that Tim Pychyl discovered makes a task procrastinationworthy:
On a neurological level, procrastination is not the slightest bit logical — it’s the result of the emotional part of your brain, your limbic system, strongarming the reasonable, rational part of your brain, your prefrontal cortex. The logical part of your brain surrenders the moment you choose Instagram over work, or decide to binge another episode of Keeping Up with the Kardashians instead of getting some sleep.
While it’s not worth spending hours listing the costs of not going for your evening run, listing the ongoing costs will significantly help for a task such as saving for retirement. Add to your list all the ways procrastinating on retirement saving could affect your social life, finances, stress, happiness, health, and so on.
In the case of Study, list the ways in which putting off study will affect you in future life. Maybe it is not getting the job you want, loss of friends, inability to complete a degree etc. Know what you want and understand how putting off certain tasks will affect you.
It’s also worth while making a list of the things you put off personally and professionally, large and small, while calculating the costs of procrastination for each. By doing this you are able to learn how to evaluate yourself, by doing this consistently, you will know when you can afford to procrastinate and when you cannot afford too.
“I have to finish this important task. It should already be done by now and I just need to do it.”
This small, seemingly innocent thought contains almost every mental block that encourages procrastination. We all use the Procrastinator’s Motto (or variations of it) every once in a while. If you’re a chronic procrastinator, chances are you repeat it to yourself very frequently — daily, perhaps.
But what’s so wrong about the Procrastinator’s Motto? In what ways do these words encourage procrastination so much — and what can we do about it? Let’s consider each part of this statement in turn, replacing each of them with an empowering alternative. In doing that, we’ll turn the original motto on its head and create a productive call to action: a “Producer’s Motto”, if you like. We’ll look into how we can rephrase this statement in point 2.
Our devices offer a mass of distractions, whether it’s email, social media, or texting with friends and family. This is especially difficult as our work becomes more ambiguous and unstructured (two triggers of procrastination).
When you notice yourself using your device to procrastinate, disconnect. Sometimes when I’m writing, I go as far as to put my phone in another room, and shut off the WiFi on my computer. Other times, I turn to an app like Freedom or Self Control, which blocks access to distracting sites, and require me to physically restart my computer to restore access.
This may sound drastic, and it is. Disabling digital distractions ahead of time gives you no choice but to study on what’s really important.
Studying too much can have many negative consequences. In the context of procrastination, allocating too much of your time to study throws your life out of balance with your values. You won’t have as much time for your friends or interests outside of college which are likely more important to you. Cal Newport describes how overworking can lead to resentment and procrastination:
Counterintuitively, working less can help your productivity over the longterm. But it’s surprisingly hard to study less, especially when you need it. It’s hard, in part, because we haven’t evolved to know exactly how much we need to study or how much we can obtain when learning.
Meditation helps you become aware of your thoughts. Becoming aware of your thoughts is an essential step to ignoring the thoughts which aren’t useful.
You don’t have to go on a big fancy retreat in order to mediate. You can start with just 510 minutes per day. You can also make a habit of being mindful throughout your day. Simply complete the steps below when you find yourself procrastinating:
Don’t try to make the thoughts go away. Don’t feel guilty for having them. Just acknowledge that they are present in your mind. Say “hello” to the thoughts. Then, choose the best course of action… and study!
I Meditate daily and it’s made a huge difference in my life. I’d recommend a mobile app such as Headspace or Calm to get you started.
Your todo list should only consist of your top 35 goals/tasks that you need to complete. Delete from your todo list those things that don’t relate to those goals/tasks.
Just say bye bye. And don’t look back!
This is important to better manage your time because with limited time, it’s important to do only things that matter most, but not every single task at hand (especially with all the potential distractions).
Do you keep avoiding study or some other big task, even though you know it will make you feel good to get it done? If so, do this:
Invite a friend over for a date to “tackle the dreaded task.”
All your friend has to do is sit in the room with you and make sure that you do the task, or if they are a really good friend, they can help.
After the task is done, you can treat you and your friend to either coffee, dessert, meal or a movie, whatever!
4. Discipline vs Procrastination
Majority of people do not have any reliable structure in their days that make it easy to be disciplined. Instead, they rely on either motivation, inspiration or willpower.
Whatever we set out to do, we often tend to think that we need to be somewhat inspired and motivated to take action. That motivation and inspiration are conditions for taking action and that the chronological order is:
Inspiration ===> Motivation ===> Action
We watch motivational videos and try to get inspired by our favorite movie or pictures of celebrities on Instagram, only to realize that this motivation is shortlived and fizzles out quickly. The amount of times I have watched Gary Vaynerchuk and been ready to build a company in a matter of seconds is way too many to count! I assume it is the same with Homework or Study, you are pumped to complete it once you have seen someone talk about completing it or actually doing it like Dr. Woo (we love him at Intellecquity!), you want to go and try it yourself.
What you need to realize is that the order of these concepts is actually the other way around.
Motivation and inspiration are created by action.
Action ===> Inspiration ===> Motivation
You do something, you start to feel inspired and then the motivation kicks in.
Have you ever had a day when you struggled with whether you should e.g. go to the gym or for a run? Tired, exhausted after work, dark and rainy outside there was no motivation and you could find any excuse to stay in.
But maybe you didn’t. Maybe it was a friend who pushed you or maybe your bag was already packed and you just went anyway, regardless of your resistance.
Do you remember the amazing feeling you had after your workout? How motivated you felt to do it again, every time? For Example, remember the first time you figured out the methodology to complete a solution? You got this rush of blood and wanted to smash out the rest of the homework… That is Action leading into Inspiration and Motivation.
This is motivation as a result of the action you took.
So how do we make sure we take action even if we are not motivated?
You have to think about willpower or discipline.
Willpower is somewhat like a muscle, a source of energy that depletes over time.
Relying only on willpower could serve in the very beginning of a new project when motivation is still very high.
Whatever goal you have set for yourself, you are excited to give it a shot and eagerly do the first steps.
Over time, however, your willpower will decrease. This depletion can be seen over the course of several days and weeks, but also in a single day, as your willpower starts off high in the morning and declines towards the evening.
At this point it will be very difficult to pack your bag for the gym, to resist that delicious pizza around the corner, or to finish that book instead of wasting time on social media.
You then wonder why you don’t have any selfdiscipline.
So both motivation and willpower are actually rather low ranking traits on the scale of consistency and productivity.
At the last stage, there will be no questioning, no laziness, you literally just do it. You would have to use willpower to not do it.
Whatever goal you have. Don’t think of the result, but rather the kind of person you have to become and the tiny steps that are needed to get there. Look back on the effective strategies above and become the person that takes action to inspire and motivate.
Reading some pages, doing some minutes of exercise, cooking a healthy meal yourself… taking small steps in the right direction on a daily basis establishes lasting habits that will ultimately shape your identity.
How do I actually stick to my habits?
By making it easy to stick to them through intelligent design of your environment.
A good example of how to use Environmental Design is your phone. The first thing many people do after waking up is to reach for their smartphone and check messages, emails or notifications from social media. This sets you in a reactive state and will prevent you from focusing on your true priorities.
Therefore, before study, intelligently design your environment.
Put your phone in airplane mode and place it somewhere impossible to reach from your desk. Prepare your todo list with the three most important things you want to achieve and place it somewhere you can see it as soon as you sit at your desk.
After completing your study, you can directly focus on rewards or other priorities that lie ahead. Should you still instinctively reach for your phone, there will be no distractions available due to the airplane mode.
This will allow you to complete your study in a productive manner instead of a reactive state. This is one of the most important aspects of productivity because remember:
“If you commit to nothing, you’ll be distracted by everything”
This has taken me roughly a week to complete. Gathering resources, finding information and collating this to make sure that it is fit for my readers. What did I learn? That I didn’t waste any time, I stuck to my schedule and didn’t miss a single second of my writing because of procrastination.
So, what does that mean?
Stop waiting until the last minute to do what you need to do. Procrastination adds stress and often leads to lowerquality work.
Start doing the things that you know you need to do in order to achieve your longterm goals. You’ll be glad you did three years from now, maybe at your dream job.
But remember, sometimes procrastinating is a rational strategy. Sometimes, it’s best to do more than just wait. When you’re not living in line with your values or you’re taking on too much study, it’s best to break it down and start.
Think critically about whether you should procrastinate, do what you need to do, or develop a new plan. Understand that it’s the habits that will drive you towards less procrastination. Habits such as putting your phone on airplane mode when you’re studying, taking regular breaks and rewarding yourself.
Happy Learning,
Solve my Math Problem… “please help me! I need this because I need to pass my exam and my homework is due tomorrow”. Sound like you? Leave everything to the last minute and you’re afraid that you’re now going to fail an exam or that your teacher is going to yell at you? Don’t worry! We have all been there!
LEAVING YOUR MATH WORK FOR THE LAST MINUTE? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
I see it time and time again students wanting help and not wanting to put in any effort to get there. I am a strong believer in learning how to do something to avoid paying for it, and I feel that is most people. As much as I disagree with the education system sometimes, I do believe that it is great that they can force people to do exams and homework to get to an end goal, which is graduation. What is see, is a massive amount of people trying to avoid learning the methods of math and still expect to graduate. Imagine if Math was like Netflix, one of your friends pays and gives all of you access… Yeah, I totally do that to! The thing with school is, you can’t have one friend pass all your Math exams for you, it sucks right! So… that means, finding a way to learn that suits you!
STRUGGLING WITH MATH? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
In 2016, my 2 friends and I joined forces to solve the problem that our brothers were facing and which turned out to be a problem that countless students around the world face to this day. “How do I get help with my Math homework/study when there’s no one around to help me?” or “I’ve got an exam in a couple of days and have no idea about this topic!”
Let’s face it. Math isn’t the easiest subject going around. Many student have faced a few hurdles, whether it be around Trigonometry or Calculus, we’ve all been there, no resources to call upon for help.
That is why we believe that no student should be left behind. Our aim is to provide students an inexpensive way to improve their math ability, a key requirement for future success, no matter where that might be.
FACING THE SAME PROBLEMS AS OTHER STUDENTS? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
If it was me, I would find every mobile app out there! Test every single one of them and find out which one suits me best. Personally, I hate the apps which charge by the minute, they are up there with my biggest HATE! If you have a question that is simple, don’t you worry, they will find out how they can draw it out a few hours! I love Mathway to be honest, (Ahhh… why is he talking about a competitor?) Because they are really good, unless they con you into their paid version! Stay Free with Mathway forever!!! They are fantastic because of their backend intelligence and Artificial Intelligence, but what can’t they do? Worded Questions… So for worded questions, you will have to look somewhere else!
Most importantly, look for help before you get to the point of “Needing” someone to help you! It will make your decisions much clearer and most likely help you learn the math problem without clouded judgement. Don’t leave learning to the last day if you want someone to solve your math problem, ask for help upfront and teach yourself how they did it using their solution. Moving forward, your schooling will become easier and that is what I am here to help with!
Math Order of Operation… What is it and how do we use it i math? “Operations” mean things like add, subtract, multiply, divide, squaring, etc. If it isn’t a number it is probably an operation.
But, when you see something like…
7 + (6 × 5^{2} + 3)
… what part should you calculate first?
Start at the left and go to the right?
Or go from right to left?
Warning: Calculate them in the wrong order, and you will get a wrong answer !
STRUGGLING WITH BODMAS? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
So, long ago people agreed to follow rules when doing calculations, and they are:
Do things in Brackets First
6 × (5 + 3)  =  6 × 8  = 
48


6 × (5 + 3)  =  30 + 3  = 
33

(wrong) 
Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract
5 × 2^{2}  =  5 × 4  = 
20


5 × 2^{2}  =  10^{2}  = 
100

(wrong) 
Multiply or Divide before you Add or Subtract
2 + 5 × 3  =  2 + 15  = 
17


2 + 5 × 3  =  7 × 3  = 
21

(wrong) 
Otherwise just go left to right
30 ÷ 5 × 3  =  6 × 3  = 
18


30 ÷ 5 × 3  =  30 ÷ 15  = 
2

(wrong) 
B

Brackets first 
O

Orders (i.e. Powers and Square Roots, etc.) 
DM

Division and Multiplication (lefttoright) 
AS

Addition and Subtraction (lefttoright) 
Divide and Multiply rank equally (and go left to right).
Add and Subtract rank equally (and go left to right)
So do it this way:
After you have done “B” and “O”, just go from left to right doing any “D” or “M” as you find them.
Then go from left to right doing any “A” or “S” as you find them.
Note: the only strange name is “Orders”. “Exponents” is used in Canada, and so you might prefer “BEDMAS”. There is also “Indices” which makes it “BIDMAS”. In the US they say “Parentheses” instead of Brackets, so it is “PEMDAS”
Multiplication before Addition:
First 6 × 2 = 12, then 3 + 12 = 15
Brackets first:
First (3 + 6) = 9, then 9 × 2 = 18
Multiplication and Division rank equally, so just go left to right:
First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3
A practical example:
Sam uses this special formula that includes gravity:
height = velocity × time − (1/2) × 9.8 × time^{2}
Sam puts in the velocity of 20 meters per second and time of 2 seconds:
height = 20 × 2 − (1/2) × 9.8 × 2^{2}
Now for the calculations!
The ball reaches 20.4 meters after 2 seconds
What about this example?
4^{32}
Exponents are special: they go topdown (do the exponent at the top first). So we calculate this way:
Start with:  4^{32}  
3^{2} = 3×3:  4^{9}  
4^{9} = 4×4×4×4×4×4×4×4×4:  262144 
And finally, what about the example from the beginning?
STRUGGLING WITH THE ORDER OF OPERATIONS? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
Happy Learning!
]]>STRUGGLING WITH MATH SYMBOLS? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
Below is a table from Rapid Tables, that can assist you with all the symbols will possibly need:
Symbol  Symbol Name  Meaning / definition  Example 

=  equals sign  equality  5 = 2+3 5 is equal to 2+3 
≠  not equal sign  inequality  5 ≠ 4 5 is not equal to 4 
≈  approximately equal  approximation  sin(0.01) ≈ 0.01, x ≈ y means x is approximately equal to y 
>  strict inequality  greater than  5 > 4 5 is greater than 4 
<  strict inequality  less than  4 < 5 4 is less than 5 
≥  inequality  greater than or equal to  5 ≥ 4, x ≥ y means x is greater than or equal to y 
≤  inequality  less than or equal to  4 ≤ 5, x ≤ y means x is less than or equal to y 
( )  parentheses  calculate expression inside first  2 × (3+5) = 16 
[ ]  brackets  calculate expression inside first  [(1+2)×(1+5)] = 18 
+  plus sign  addition  1 + 1 = 2 
−  minus sign  subtraction  2 − 1 = 1 
±  plus – minus  both plus and minus operations  3 ± 5 = 8 and 2 
±  minus – plus  both minus and plus operations  3 ∓ 5 = 2 and 8 
*  asterisk  multiplication  2 * 3 = 6 
×  times sign  multiplication  2 × 3 = 6 
⋅  multiplication dot  multiplication  2 ⋅ 3 = 6 
÷  division sign / obelus  division  6 ÷ 2 = 3 
/  division slash  division  6 / 2 = 3 
—  horizontal line  division / fraction  
mod  modulo  remainder calculation  7 mod 2 = 1 
.  period  decimal point, decimal separator  2.56 = 2+56/100 
a^{b}  power  exponent  2^{3 }= 8 
a^b  caret  exponent  2 ^ 3^{ }= 8 
√a  square root 
√a ⋅ √a = a 
√9 = ±3 
^{3}√a  cube root  ^{3}√a ⋅ ^{3}√a ⋅ ^{3}√a = a  ^{3}√8 = 2 
^{4}√a  fourth root  ^{4}√a ⋅ ^{4}√a ⋅ ^{4}√a ⋅ ^{4}√a = a  ^{4}√16 = ±2 
^{n}√a  nth root (radical)  for n=3, ^{n}√8 = 2  
%  percent  1% = 1/100  10% × 30 = 3 
‰  permille  1‰ = 1/1000 = 0.1%  10‰ × 30 = 0.3 
ppm  permillion  1ppm = 1/1000000  10ppm × 30 = 0.0003 
ppb  perbillion  1ppb = 1/1000000000  10ppb × 30 = 3×10^{7} 
ppt  pertrillion  1ppt = 10^{12}  10ppt × 30 = 3×10^{10} 
Symbol  Symbol Name  Meaning / definition  Example 

∠  angle  formed by two rays  ∠ABC = 30° 
measured angle  ABC = 30°  
spherical angle  AOB = 30°  
∟  right angle  = 90°  α = 90° 
°  degree  1 turn = 360°  α = 60° 
deg  degree  1 turn = 360deg  α = 60deg 
′  prime  arcminute, 1° = 60′  α = 60°59′ 
″  double prime  arcsecond, 1′ = 60″  α = 60°59′59″ 
line  infinite line  
AB  line segment  line from point A to point B  
ray  line that start from point A  
arc  arc from point A to point B  = 60°  
⊥  perpendicular  perpendicular lines (90° angle)  AC ⊥ BC 
∥  parallel  parallel lines  AB ∥ CD 
≅  congruent to  equivalence of geometric shapes and size  ∆ABC≅ ∆XYZ 
~  similarity  same shapes, not same size  ∆ABC~ ∆XYZ 
Δ  triangle  triangle shape  ΔABC≅ ΔBCD 
x–y  distance  distance between points x and y   x–y  = 5 
π  pi constant  π = 3.141592654…is the ratio between the circumference and diameter of a circle  c = π⋅d = 2⋅π⋅r 
rad  radians  radians angle unit  360° = 2π rad 
^{c}  radians  radians angle unit  360° = 2π ^{c} 
grad  gradians / gons  grads angle unit  360° = 400 grad 
^{g}  gradians / gons  grads angle unit  360° = 400 ^{g} 
Symbol  Symbol Name  Meaning / definition  Example 

x  x variable  unknown value to find  when 2x = 4, then x = 2 
≡  equivalence  identical to  
≜  equal by definition  equal by definition  
:=  equal by definition  equal by definition  
~  approximately equal  weak approximation  11 ~ 10 
≈  approximately equal  approximation  sin(0.01) ≈ 0.01 
∝  proportional to  proportional to 
y ∝ x when y = kx, kconstant 
∞  lemniscate  infinity symbol  
≪  much less than  much less than  1 ≪ 1000000 
≫  much greater than  much greater than  1000000 ≫ 1 
( )  parentheses  calculate expression inside first  2 * (3+5) = 16 
[ ]  brackets  calculate expression inside first  [(1+2)*(1+5)] = 18 
{ }  braces  set  
⌊x⌋  floor brackets  rounds number to lower integer  ⌊4.3⌋ = 4 
⌈x⌉  ceiling brackets  rounds number to upper integer  ⌈4.3⌉ = 5 
x!  exclamation mark  factorial  4! = 1*2*3*4 = 24 
 x   single vertical bar  absolute value   5  = 5 
f (x)  function of x  maps values of x to f(x)  f (x) = 3x+5 
(f ∘ g)  function composition  (f ∘ g) (x) = f (g(x))  f (x)=3x,g(x)=x1 ⇒(f ∘ g)(x)=3(x1) 
(a,b)  open interval  (a,b) = {x  a < x < b}  x∈ (2,6) 
[a,b]  closed interval  [a,b] = {x  a ≤ x ≤ b}  x ∈ [2,6] 
∆  delta  change / difference  ∆t = t_{1 }– t_{0} 
∆  discriminant  Δ = b^{2} – 4ac  
∑  sigma  summation – sum of all values in range of series  ∑ x_{i}= x_{1}+x_{2}+…+x_{n} 
∑∑  sigma  double summation  
∏  capital pi  product – product of all values in range of series  ∏ x_{i}=x_{1}∙x_{2}∙…∙x_{n} 
e  e constant / Euler’s number  e = 2.718281828…  e = lim (1+1/x)^{x} , x→∞ 
γ  EulerMascheroni constant  γ = 0.5772156649…  
φ  golden ratio  golden ratio constant  
π  pi constant  π = 3.141592654…is the ratio between the circumference and diameter of a circle  c = π⋅d = 2⋅π⋅r 
Symbol  Symbol Name  Meaning / definition  Example 

·  dot  scalar product  a · b 
×  cross  vector product  a × b 
A⊗B  tensor product  tensor product of A and B  A ⊗ B 
inner product  
[ ]  brackets  matrix of numbers  
( )  parentheses  matrix of numbers  
 A   determinant  determinant of matrix A  
det(A)  determinant  determinant of matrix A  
 x   double vertical bars  norm  
A^{T}  transpose  matrix transpose  (A^{T})_{ij} = (A)_{ji} 
A^{†}  Hermitian matrix  matrix conjugate transpose  (A^{†})_{ij} = (A)_{ji} 
A^{*}  Hermitian matrix  matrix conjugate transpose  (A^{*})_{ij} = (A)_{ji} 
A^{ 1}  inverse matrix  A A^{1} = I  
rank(A)  matrix rank  rank of matrix A  rank(A) = 3 
dim(U)  dimension  dimension of matrix A  dim(U) = 3 
Symbol  Symbol Name  Meaning / definition  Example 

P(A)  probability function  probability of event A  P(A) = 0.5 
P(A ∩ B)  probability of events intersection  probability that of events A and B  P(A∩B) = 0.5 
P(A ∪ B)  probability of events union  probability that of events A or B  P(A∪B) = 0.5 
P(A  B)  conditional probability function  probability of event A given event B occured  P(A  B) = 0.3 
f (x)  probability density function (pdf)  P(a ≤ x ≤ b) = ∫ f (x) dx  
F(x)  cumulative distribution function (cdf)  F(x) = P(X≤ x)  
μ  population mean  mean of population values  μ = 10 
E(X)  expectation value  expected value of random variable X  E(X) = 10 
E(X  Y)  conditional expectation  expected value of random variable X given Y  E(X  Y=2) = 5 
var(X)  variance  variance of random variable X  var(X) = 4 
σ^{2}  variance  variance of population values  σ^{2 }= 4 
std(X)  standard deviation  standard deviation of random variable X  std(X) = 2 
σ_{X}  standard deviation  standard deviation value of random variable X  σ_{X}_{ }= 2 
median  middle value of random variable x  
cov(X,Y)  covariance  covariance of random variables X and Y  cov(X,Y) = 4 
corr(X,Y)  correlation  correlation of random variables X and Y  corr(X,Y) = 0.6 
ρ_{X,Y}  correlation  correlation of random variables X and Y  ρ_{X,Y} = 0.6 
∑  summation  summation – sum of all values in range of series  
∑∑  double summation  double summation  
Mo  mode  value that occurs most frequently in population  
MR  midrange  MR = (x_{max}+x_{min})/2  
Md  sample median  half the population is below this value  
Q_{1}  lower / first quartile  25% of population are below this value  
Q_{2}  median / second quartile  50% of population are below this value = median of samples  
Q_{3}  upper / third quartile  75% of population are below this value  
x  sample mean  average / arithmetic mean  x = (2+5+9) / 3 = 5.333 
s_{ }^{2}  sample variance  population samples variance estimator  s^{ }^{2} = 4 
s  sample standard deviation  population samples standard deviation estimator  s = 2 
z_{x}  standard score  z_{x} = (xx) / s_{x}  
X ~  distribution of X  distribution of random variable X  X ~ N(0,3) 
N(μ,σ^{2})  normal distribution  gaussian distribution  X ~ N(0,3) 
U(a,b)  uniform distribution  equal probability in range a,b  X ~ U(0,3) 
exp(λ)  exponential distribution  f (x) = λe^{–λx} , x≥0  
gamma(c, λ)  gamma distribution  f (x) = λ c x^{c1}e^{–λx} / Γ(c), x≥0  
χ^{ 2}(k)  chisquare distribution  f (x) = x^{k}^{/21}e^{–x/2} / ( 2^{k/2 }Γ(k/2) )  
F (k_{1}, k_{2})  F distribution  
Bin(n,p)  binomial distribution  f (k) = _{n}C_{k} p^{k}(1p)^{nk}  
Poisson(λ)  Poisson distribution  f (k) = λ^{k}e^{–λ} / k!  
Geom(p)  geometric distribution  f (k) = p(1p)^{ k}  
HG(N,K,n)  hypergeometric distribution  
Bern(p)  Bernoulli distribution 
Symbol  Symbol Name  Meaning / definition  Example 

n!  factorial  n! = 1⋅2⋅3⋅…⋅n  5! = 1⋅2⋅3⋅4⋅5 = 120 
_{n}P_{k}  permutation  _{5}P_{3} = 5! / (53)! = 60  
_{n}C_{k}  combination  _{5}C_{3} = 5!/[3!(53)!]=10 
Symbol  Symbol Name  Meaning / definition  Example 

{ }  set  a collection of elements  A = {3,7,9,14}, B = {9,14,28} 
A ∩ B  intersection  objects that belong to set A and set B  A ∩ B = {9,14} 
A ∪ B  union  objects that belong to set A or set B  A ∪ B = {3,7,9,14,28} 
A ⊆ B  subset  A is a subset of B. set A is included in set B.  {9,14,28} ⊆ {9,14,28} 
A ⊂ B  proper subset / strict subset  A is a subset of B, but A is not equal to B.  {9,14} ⊂ {9,14,28} 
A ⊄ B  not subset  set A is not a subset of set B  {9,66} ⊄ {9,14,28} 
A ⊇ B  superset  A is a superset of B. set A includes set B  {9,14,28} ⊇ {9,14,28} 
A ⊃ B  proper superset / strict superset  A is a superset of B, but B is not equal to A.  {9,14,28} ⊃ {9,14} 
A ⊅ B  not superset  set A is not a superset of set B  {9,14,28} ⊅ {9,66} 
2^{A}  power set  all subsets of A  
power set  all subsets of A  
A = B  equality  both sets have the same members  A={3,9,14}, B={3,9,14}, A=B 
A^{c}  complement  all the objects that do not belong to set A  
A \ B  relative complement  objects that belong to A and not to B  A = {3,9,14}, B = {1,2,3}, AB = {9,14} 
A – B  relative complement  objects that belong to A and not to B  A = {3,9,14}, B = {1,2,3}, AB = {9,14} 
A ∆ B  symmetric difference  objects that belong to A or B but not to their intersection  A = {3,9,14}, B = {1,2,3}, A ∆ B = {1,2,9,14} 
A ⊖ B  symmetric difference  objects that belong to A or B but not to their intersection  A = {3,9,14}, B = {1,2,3}, A ⊖ B = {1,2,9,14} 
a∈A  element of, belongs to 
set membership  A={3,9,14}, 3 ∈ A 
x∉A  not element of  no set membership  A={3,9,14}, 1 ∉ A 
(a,b)  ordered pair  collection of 2 elements  
A×B  cartesian product  set of all ordered pairs from A and B  
A  cardinality  the number of elements of set A  A={3,9,14}, A=3 
#A  cardinality  the number of elements of set A  A={3,9,14}, #A=3 
alephnull  infinite cardinality of natural numbers set  
alephone  cardinality of countable ordinal numbers set  
Ø  empty set  Ø = { }  C = {Ø} 
universal set  set of all possible values  
_{0}  natural numbers / whole numbers set (with zero)  _{0} = {0,1,2,3,4,…}  0 ∈ _{0} 
_{1}  natural numbers / whole numbers set (without zero)  _{1} = {1,2,3,4,5,…}  6 ∈ _{1} 
integer numbers set  = {…3,2,1,0,1,2,3,…}  6 ∈  
rational numbers set  = {x  x=a/b, a,b∈}  2/6 ∈  
real numbers set  = {x  ∞ < x <∞}  6.343434∈  
complex numbers set  = {z  z=a+bi, ∞<a<∞, ∞<b<∞}  6+2i ∈ 
Symbol  Symbol Name  Meaning / definition  Example 

⋅  and  and  x ⋅ y 
^  caret / circumflex  and  x ^ y 
&  ampersand  and  x & y 
+  plus  or  x + y 
∨  reversed caret  or  x ∨ y 
  vertical line  or  x  y 
x‘  single quote  not – negation  x‘ 
x  bar  not – negation  x 
¬  not  not – negation  ¬ x 
!  exclamation mark  not – negation  ! x 
⊕  circled plus / oplus  exclusive or – xor  x ⊕ y 
~  tilde  negation  ~ x 
⇒  implies  
⇔  equivalent  if and only if (iff)  
equivalent  if and only if (iff)  
∀  for all  
∃  there exists  
∄  there does not exists  
∴  therefore  
∵  because / since 
Symbol  Symbol Name  Meaning / definition  Example 

limit  limit value of a function  
ε  epsilon  represents a very small number, near zero  ε → 0 
e  e constant / Euler’s number  e = 2.718281828…  e = lim (1+1/x)^{x}, x→∞ 
y ‘  derivative  derivative – Lagrange’s notation  (3x^{3})’ = 9x^{2} 
y ”  second derivative  derivative of derivative  (3x^{3})” = 18x 
y^{(n)}  nth derivative  n times derivation  (3x^{3})^{(3)} = 18 
derivative  derivative – Leibniz’s notation  d(3x^{3})/dx = 9x^{2}  
second derivative  derivative of derivative  d^{2}(3x^{3})/dx^{2} = 18x  
nth derivative  n times derivation  
time derivative  derivative by time – Newton’s notation  
time second derivative  derivative of derivative  
D_{x }y  derivative  derivative – Euler’s notation  
D_{x}^{2}y  second derivative  derivative of derivative  
partial derivative  ∂(x^{2}+y^{2})/∂x = 2x  
∫  integral  opposite to derivation  ∫ f(x)dx 
∫∫  double integral  integration of function of 2 variables  ∫∫ f(x,y)dxdy 
∫∫∫  triple integral  integration of function of 3 variables  ∫∫∫ f(x,y,z)dxdydz 
∮  closed contour / line integral  
∯  closed surface integral  
∰  closed volume integral  
[a,b]  closed interval  [a,b] = {x  a ≤ x ≤ b}  
(a,b)  open interval  (a,b) = {x  a < x < b}  
i  imaginary unit  i ≡ √1  z = 3 + 2i 
z*  complex conjugate  z = a+bi → z*=a–bi  z* = 3 – 2i 
z  complex conjugate  z = a+bi → z = a–bi  z = 3 – 2i 
∇  nabla / del  gradient / divergence operator  ∇f (x,y,z) 
vector  
unit vector  
x * y  convolution  y(t) = x(t) * h(t)  
Laplace transform  F(s) = {f (t)}  
Fourier transform  X(ω) = {f (t)}  
δ  delta function  
∞  lemniscate  infinity symbol 
Name  European  Roman  Hindu Arabic  Hebrew 

zero  0  ٠  
one  1  I  ١  א 
two  2  II  ٢  ב 
three  3  III  ٣  ג 
four  4  IV  ٤  ד 
five  5  V  ٥  ה 
six  6  VI  ٦  ו 
seven  7  VII  ٧  ז 
eight  8  VIII  ٨  ח 
nine  9  IX  ٩  ט 
ten  10  X  ١٠  י 
eleven  11  XI  ١١  יא 
twelve  12  XII  ١٢  יב 
thirteen  13  XIII  ١٣  יג 
fourteen  14  XIV  ١٤  יד 
fifteen  15  XV  ١٥  טו 
sixteen  16  XVI  ١٦  טז 
seventeen  17  XVII  ١٧  יז 
eighteen  18  XVIII  ١٨  יח 
nineteen  19  XIX  ١٩  יט 
twenty  20  XX  ٢٠  כ 
thirty  30  XXX  ٣٠  ל 
forty  40  XL  ٤٠  מ 
fifty  50  L  ٥٠  נ 
sixty  60  LX  ٦٠  ס 
seventy  70  LXX  ٧٠  ע 
eighty  80  LXXX  ٨٠  פ 
ninety  90  XC  ٩٠  צ 
one hundred  100  C  ١٠٠  ק 
Upper Case Letter  Lower Case Letter  Greek Letter Name  English Equivalent  Letter Name Pronounce 

Α  α  Alpha  a  alfa 
Β  β  Beta  b  beta 
Γ  γ  Gamma  g  gama 
Δ  δ  Delta  d  delta 
Ε  ε  Epsilon  e  epsilon 
Ζ  ζ  Zeta  z  zeta 
Η  η  Eta  h  ehta 
Θ  θ  Theta  th  teta 
Ι  ι  Iota  i  iota 
Κ  κ  Kappa  k  kapa 
Λ  λ  Lambda  l  lamda 
Μ  μ  Mu  m  myoo 
Ν  ν  Nu  n  noo 
Ξ  ξ  Xi  x  xee 
Ο  ο  Omicron  o  omeecron 
Π  π  Pi  p  payee 
Ρ  ρ  Rho  r  row 
Σ  σ  Sigma  s  sigma 
Τ  τ  Tau  t  taoo 
Υ  υ  Upsilon  u  oopsilon 
Φ  φ  Phi  ph  fee 
Χ  χ  Chi  ch  khee 
Ψ  ψ  Psi  ps  psee 
Ω  ω  Omega  o  omega 
Number  Roman numeral 

0  not defined 
1  I 
2  II 
3  III 
4  IV 
5  V 
6  VI 
7  VII 
8  VIII 
9  IX 
10  X 
11  XI 
12  XII 
13  XIII 
14  XIV 
15  XV 
16  XVI 
17  XVII 
18  XVIII 
19  XIX 
20  XX 
30  XXX 
40  XL 
50  L 
60  LX 
70  LXX 
80  LXXX 
90  XC 
100  C 
200  CC 
300  CCC 
400  CD 
500  D 
600  DC 
700  DCC 
800  DCCC 
900  CM 
1000  M 
5000  V 
10000  X 
50000  L 
100000  C 
500000  D 
1000000  M 
STRUGGLING WITH COLLEGE MATH? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
Need some assistance finding the best Math Problem Solvers?
Here at Intellecquity, we here about our “competitors” all the time. These businesses set out to do the same as us here at Intellecquity, which is, to provide help and value to students in need. In this article, I have named the Applications I believe that you should look at and have a try of if you are looking for some help with a Math problem solver.
Here are the best Math Problem Solvers I believe are in the Market now!
With millions of users and billions of problems solved, Mathway is the world’s #1 math problem solver. From basic algebra to complex calculus, Mathway instantly solves your most difficult math problems – simply type your problem in (or point your camera and snap a pic!) to receive instant free answers. The only concern with Mathway that I have is that it is expensive for the services they offer, especially when you get answers with no working. It is a concern when Mathway doesn’t provide working out for students as they will never learn how to work out solutions themselves.
https://www.mathway.com
Students have access to the program 24/7 at the touch of a button. Students can work with our tutors for 17 minutes, or 2.5 hours, all for the same flat rate. Make sure that you use this a lot as it becomes very expensive if you don’t study a lot. Be cautious with the per minute pricing as well! When you expect a question to be answered quickly, it can be drawn out. None the less, if you are looking for chat based tutoring, Yup is a viable option.
https://www.yup.com/
STRUGGLING WITH MATH? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
Intellecquity… the only imaged based tutoring app I know of. Pay per question and no perminute pricing or subscriptions to lock you in. As we continually improve Intellecquity, we have 3 things in mind for our students – Quality, Speed and Price.
Take a picture of a homework problem and they have incorporated AI (Artificial Intelligence) which instantly figures out which concepts you need to learn in order to answer it!
Socratic’s AI combines cuttingedge computer vision technologies, which read questions from images, with machine learning classifiers built using millions of sample homework questions, to accurately predict which concepts will help you solve your question. It is a great app that can be used on a regular basis, and like all the Math Problem Solvers on this page, I believe all of them should be tried.
Brainly is currently the world’s largest social learning community! 80 million students use Brainly every month. That is 60 million study partners to help you with any school subject, such as Math, Social Studies, Science, English, Foreign Languages and many more.
• Free – Brainly is 100% free of charge!
• 24/7 – Unlimited access, anywhere, anytime
• Share Your Knowledge – Earn points and gain ranks by helping other students
Brainly is an exceptional platform with lots of students which can help you for free, as long as you help someone else first. This means that you have to provide help with someone else’s homework before you can receive assistance with yours. Additionally, I have tested Brainly and know that not all questions I have asked are properly answered because they are just others students trying to get credits to be able to ask their own questions.
All in all, these are the best Math Problem Solvers in the Market right now, I believe. If you are studying or looking around, test all these out! As always be careful of “FreeTrials” where they make you put your card details in first.
Until next time,
The Intellecquity Team
Well, What are you looking for? Do you want something that will help you find a Tutor to teach you math, do you want an app that utilizes artificial intelligence to give you the answer for a question you can’t figure out, do you want an app that allows you to chat to a tutor like a messenger application or do you want an app that allows you to send images?
STRUGGLING WITH MATH? Get the assistance, ongoing support and tutors you need to learn faster, make fewer mistakes and get the grades you deserve. Learn More.
There are several offerings in the Market these days and I can help point you in the direction of a few!
The Vygo platform unlocks private tutoring so all university students can get the most out of their degrees. Vygo attracts tutors from all faculties who only tutor classes they’ve aced themselves. Tutors set their own rates and are half the price of traditional tutoring (on average). Students can book sessions when and where they need them (online and inperson).
With millions of users and billions of problems solved, Mathway is the world’s #1 math problem solver. From basic algebra to complex calculus, Mathway instantly solves your most difficult math problems – simply type your problem in (or point your camera and snap a pic!) to receive instant free answers. The only concern with Mathway that I have is that it is expensive for the services they offer, especially when you get answers with no working. It is a concern when Mathway doesn’t provide working out for students as they will never learn how to work out solutions themselves.
https://www.mathway.com
Students have access to the program 24/7 at the touch of a button. Students can work with our tutors for 17 minutes, or 2.5 hours, all for the same flat rate. Make sure that you use this a lot as it becomes very expensive if you don’t study a lot. Be cautious with the per minute pricing as well! When you expect a question to be answered quickly, it can be drawn out. None the less, if you are looking for chat based tutoring, Yup is a viable option.
https://www.yup.com/
Intellecquity… the only imaged based tutoring app I know of. Pay per question and no perminute pricing or subscriptions to lock you in. As we continually improve Intellecquity, we have 3 things in mind for our students – Quality, Speed and Price.
]]>Well, What are you looking for? Do you want something that will help you find a Tutor to teach you math, do you want an app that utilizes artificial intelligence to give you the answer for a question you can’t figure out, do you want an app that allows you to chat to a tutor like a messenger application or do you want an app that allows you to send images?
There are several offerings in the Market these days and I can help point you in the direction of a few!
The Vygo platform unlocks private tutoring so all university students can get the most out of their degrees. Vygo attracts tutors from all faculties who only tutor classes they’ve aced themselves. Tutors set their own rates and are half the price of traditional tutoring (on average). Students can book sessions when and where they need them (online and inperson).
With millions of users and billions of problems solved, Mathway is the world’s #1 math problem solver. From basic algebra to complex calculus, Mathway instantly solves your most difficult math problems – simply type your problem in (or point your camera and snap a pic!) to receive instant free answers. The only concern with Mathway that I have is that it is expensive for the services they offer, especially when you get answers with no working. It is a concern when Mathway doesn’t provide working out for students as they will never learn how to work out solutions themselves.
https://www.mathway.com
Students have access to the program 24/7 at the touch of a button. Students can work with our tutors for 17 minutes, or 2.5 hours, all for the same flat rate. Make sure that you use this a lot as it becomes very expensive if you don’t study a lot. Be cautious with the per minute pricing as well! When you expect a question to be answered quickly, it can be drawn out. None the less, if you are looking for chat based tutoring, Yup is a viable option.
https://www.yup.com/
Intellecquity… the only imaged based tutoring app I know of. Pay per question and no perminute pricing or subscriptions to lock you in. As we continually improve Intellecquity, we have 3 things in mind for our students – Quality, Speed and Price.
]]>Well, What are you looking for? Do you want something that will help you find a Tutor to teach you math, do you want an app that utilizes artificial intelligence to give you the answer for a question you can’t figure out, do you want an app that allows you to chat to a tutor like a messenger application or do you want an app that allows you to send images?
There are several offerings in the Market these days and I can help point you in the direction of a few!
The Vygo platform unlocks private tutoring so all university students can get the most out of their degrees. Vygo attracts tutors from all faculties who only tutor classes they’ve aced themselves. Tutors set their own rates and are half the price of traditional tutoring (on average). Students can book sessions when and where they need them (online and inperson).
With millions of users and billions of problems solved, Mathway is the world’s #1 math problem solver. From basic algebra to complex calculus, Mathway instantly solves your most difficult math problems – simply type your problem in (or point your camera and snap a pic!) to receive instant free answers. The only concern with Mathway that I have is that it is expensive for the services they offer, especially when you get answers with no working. It is a concern when Mathway doesn’t provide working out for students as they will never learn how to work out solutions themselves.
https://www.mathway.com
Students have access to the program 24/7 at the touch of a button. Students can work with our tutors for 17 minutes, or 2.5 hours, all for the same flat rate. Make sure that you use this a lot as it becomes very expensive if you don’t study a lot. Be cautious with the per minute pricing as well! When you expect a question to be answered quickly, it can be drawn out. None the less, if you are looking for chat based tutoring, Yup is a viable option.
https://www.yup.com/
Intellecquity… the only imaged based tutoring app I know of. Pay per question and no perminute pricing or subscriptions to lock you in. As we continually improve Intellecquity, we have 3 things in mind for our students – Quality, Speed and Price.
]]>Well, What are you looking for? Do you want something that will help you find a Tutor to teach you math, do you want an app that utilizes artificial intelligence to give you the answer for a question you can’t figure out, do you want an app that allows you to chat to a tutor like a messenger application or do you want an app that allows you to send images?
There are several offerings in the Market these days and I can help point you in the direction of a few!
The Vygo platform unlocks private tutoring so all university students can get the most out of their degrees. Vygo attracts tutors from all faculties who only tutor classes they’ve aced themselves. Tutors set their own rates and are half the price of traditional tutoring (on average). Students can book sessions when and where they need them (online and inperson).
With millions of users and billions of problems solved, Mathway is the world’s #1 math problem solver. From basic algebra to complex calculus, Mathway instantly solves your most difficult math problems – simply type your problem in (or point your camera and snap a pic!) to receive instant free answers. The only concern with Mathway that I have is that it is expensive for the services they offer, especially when you get answers with no working. It is a concern when Mathway doesn’t provide working out for students as they will never learn how to work out solutions themselves.
https://www.mathway.com
Students have access to the program 24/7 at the touch of a button. Students can work with our tutors for 17 minutes, or 2.5 hours, all for the same flat rate. Make sure that you use this a lot as it becomes very expensive if you don’t study a lot. Be cautious with the per minute pricing as well! When you expect a question to be answered quickly, it can be drawn out. None the less, if you are looking for chat based tutoring, Yup is a viable option.
https://www.yup.com/
Intellecquity… the only imaged based tutoring app I know of. Pay per question and no perminute pricing or subscriptions to lock you in. As we continually improve Intellecquity, we have 3 things in mind for our students – Quality, Speed and Price.
]]>
When doing your homework, you want a couple of things;
Would you agree with the three above? As well as in that order?
1. Speed of Response is Key as we don’t do our homework over 7 days. Majority of students will Study for 12 hours, 3 days a week. This means that you need help when you are studying not when someone else can help you of “fit you in”. Tutors have such control of when you can study, how you study and what you study. Does that help you with your homework question that you have tomorrow, possibly, if the curriculum you are learning at school matches up with your tutor.
2. Quality of Response is next as it determines how well you learn and reciprocate your understanding from a tutor or teacher. What happens if the person you are being taught by doesn’t understand how you best learn or tries to provide your education that takes Months of learning into a 1hr session a week? It doesn’t work and they are not going to help you for 3hrs at the price of 1hr to make sure the solution they provide you is Quality. If your solution provided by the person teaching you isn’t quality, how can you be expected to provide quality answers in the future? Quality is the foundation of Learning, especially for Mathematics.
3. Price of Assistance is last on the list for a couple of reason, I am not saying it doesn’t matter, I am just saying that for education, quality and speed are more important. If someone provides you with a good solution in a reasonably quick manner, they deserve to be paid for their time and effort. I believe that Online tutoring and Mobile tutoring is the future, which is why I founded Intellecquity.
Overall, I don’t believe that these 3 key factors can be met with standard tuition. It is outdated and doesn’t provide the value of Online and Mobile Tutoring. How can A tutor who meets you once a week (at best) assist you when you are doing your homework, how can they assist while not using up the entire hour session with out going over the session length and lastly how can they charge such hefty fees of $50 & up for an hour session.
If your looking for help with your homework, look at my favourites: