How do I apply algebra/calculus to everyday problems in my life?

Question

I am still a senior in high school and want to major in computer science when I go to college this fall. I still struggle to see how algebra and calculus is really used to solve problems in the world. I have never been a big fan of mathematics because I fail to see where it is useful. I've been told it's used in almost everything but that was too vague of an explanation for me. For me personally, if I do not see something as useful in, I blow over it, that's why my math grades for the last 4 years have been average at best. I haven't really been interested in it a whole lot as much as I am interested in programming languages and the computers. Again, I know mathematics was used in the making of both of those things but I feel I was taught mathematics by my teacher for sake of knowing it but never really applied it to anything in my life at all. A lot of people around me say they like math and doing all sorts of calculations, but I fail to see their interest.

The point of this is that I WANT to like math and understand it more than as something I need to know to get a better grade in school. I am afraid of getting to college and question why I am spending money on something, I feel as of now, isn't relevant to my interests. I still don't see the connection between it and other fields. Are there any eye opening articles or problems you recommend me to look at to get a better understanding of it all?

Anything at all is appreciated, I've had this problem for the longest time and I don't want to get myself into something I'm not completely comfortable with.

HS

Answer 1

I don't think you need an article, but a change of attitude. Education is about self improvement. If you don't want to improve, then don't clutter up our schools. Asking how math is used in real life is like a football player asking the coach when he's going to do a push-up in a game. He not. The push-ups make him strong and he uses his strength in the game. Learning deep math makes your brain strong. Maybe you never do calculus in your job, but you do your job well because your brain isn't all mushy.

I wonder if you see the Catch-22. In order to understand how valuable the math is, you have to know the math. Either trust those who are older and wiser or take your chances.

Answer 2

So firstly you yourself agreed with the fact that your computer and programming languages are weaved through with mathematics, but try to think about the house you live in it is also built using mathematics. When you go to school you may cross some streets with streetlights, how frequently they turn red is also a careful calcualtion considering the traffic in the area and the time of the day. Even where the roads are (or at least should be) is a result of calculations. When you take out money from an ATM you expect your credit card to work safely, the communication between the ATM and the bank is encrypted once again using really sophisticated mathematics (namely integer factorisation and discrete logarithms or a combination of those, altough this may change in the next decade). When you download files from the web you would like to be able to know whether it is the actual file you wanted or not, this is also done by sophisticated algorythms called hash functions. I recently read some papers about how the DNA is located in the nucleus and it used so called "knot theory" which is a part of mathematics called topology. Classical phisics is literally impossible without mathematics, Newtons and Keplers laws are impossible without calculus and geometry. Even modern particle physics uses abstract algebra to exhibit some symmetries when particles do their things, as you see I am not an expert on particle phisics but I am really interested in group theory which they use to their aid. A really modern part of mathematics called cathegory theory helps a lot with computer scinces, helping to decide what is computable and what is not etc. As you see already or may not yet see but if we would remove the mathematical accomplishments of the last, say $200$ years we would go back to the cave with a pointy spear in our hand.

When you think about it it is almost the opposite and hard to find something that is not the product of modern mathematics.

Altough I absolutely understand your claim that "low-level" or high school mathematics feels a bit, hmmm how to put it? a bit like you have to do it because someone decided that you need an grade in it. But most of mathematics you learn in low level is usually good only in the grocery shop to estimate how much you will pay.

I worked as a teacher in high school and I felt the same as you, it can be a good training for the brain but it feels colourless, dry and VERY repetitive. This is mostly because it is an unfamiliar territory for our brain and we need to train up our brain to be able to think mathematically. Let me explain this with an example. Language is something we use a lot hence we train it a lot. Lets say I would like to learn english. Do you think it would be a good exercise for me to write down the word CAR on million times? Certainly not since language is not about one word, it is about how I weave together many words to form sentences and further to form sentences to express my feelings and thoughts. But the letter C,A,R and the word CAR is necessary to be able to talk in english, these are the building blocks but not the point of language. In the same way addition and multiplication and numbers are not the point but the building blocks of mathematics and we use these building blocks to build conclusions and logical decisions. But we are not using these building blocks as often as we use language, that is why we have to train a lot using them.

You can think at everything you so far learned in school about mathematics as a super small special case of a huge and beatiful abstract theory. But to be able to explore this abstract word you need your brain trained in this special case.

Sorry for the lenghty answer but I couldn´t explain this shorter.

P.S.: if you will study computer science at university you still will be required to explore this wonderful world (a bit at least) and good luck I hope I could help a bit.

Answer 3

The following answer is a subjective of the author about applied math

First of all, I don't think this is a bad question. When I was a young math student in calculus / linear algebra I used to walk home from school and look around trying to figure out what kinds of problems I could solve with my math skills that other people couldn't, and was usually disappointed that I couldn't come up with much other than calculating volumes of weird shapes.

Learning math with the aim of solving real world problems isn't like going to trade school with the aim of doing real world work. Trade school you go learn a skill-set and it is very clear how you will be applying it and what problems you can solve with it. Then (more or less) you will use that exact skill repetitively for the rest of your life. Learning math to solve real world problems is more like building an abstract tool kit of problem solving skills so that hopefully no matter what problem arises, we can abstract the problem into a purely mathematical question for which the answer is already known, or we have skills to approach the problem and find a new answer.

In reality there isn't a long list of obvious problems and applications that crop up in daily life that math people can do, and non math people can't. I live in a big city and I have a graduate degree in math and I would say I get by in life just as well as other intelligent people who don't have a background in math. However, it would be false to say that the modern and complicated world we live in is not dense with complicated mathematical processes going on all around us. Part of the reason that the applications around us aren't so visible is that applying math in the real world can be really, really complicated. The real world is not always as concise and black and white like the world where pure mathematics takes place. Also, a lot of the complicated math problems in daily life have already been solved and are taking place 'behind the scenes' and we just aren't giving thought to them.

Here are some example:

• The app 'Shazam' where you play a song and it returns the name uses very advanced fourier analysis to work. Because I have a graduate degree in math I am able to read about this technology and have a decent understanding of how it works, where for an ordinary person it might as well be magic.
• I have heard that the scheduling for sports teams (I am not sure if it is football, basketball, or baseball.. I think basketball?) is a very complicated problem. Apparently the people who come up with the schedule are using advanced mathematical methods and are making big money.
• Ask an ordinary person this question: "If you have 12 sweaters in your closet, but you can only pack 5 for vacation, how many ways are there to pick 5 sweaters? Now what if 2 of the 12 sweaters are indistinguishable". Time them and see how long it takes. Now ask someone with a math degree.

• Someone from the county office once called my professor and said they were unloading some big concrete structures and wanted to know where to push it (with a tractor or something) so that it would move of the loading dock without spinning (this is known as center of mass). They didn't have a clue how to go about this, and the stakes were high because they told us each structure was worth about \$50k USD. I happened to be in her office, we had them estimate the density function and we set up the triple integral and gave them their answer.

• Imagine that you are of the age where you have a credit card. Suppose you have \$2000 worth of charges on your account, the monthly interest is 12%, and you don't plan to make any more charges. The minimum payment is \$52 a month. You are interested in comparing outcomes for different monthly payments. Try to find a closed form function for the balance at month $n$ based on paying a monthly payment of $m$ dollars. Use these functions to compare total interest paid. This is something the average person who hasn't studied math would not be able to do. Most of my pre-calc students could not do this without brute forcing it.

• Advances in math are often very useful to other academic fields. Orbital symmetries became very important in chemistry at some point in time, and suddenly a lot of questions in chemistry could be answered by knowing group theory, and fortunately mathematicians had already developed group theory extensively so chemistry advanced very quickly. In an even more abstract example, string theory likes to make use of algebraic geometry.
• Look up the famous 7 bridges problem. This solution answers a very concrete real world problem but is solved purely mathematically.
• A lot of cyber security is dependent on hash algorithms. The common one being implemented right now, I think, is called SHA-256. The idea is that the algorithm ought to take in strings of arbitrary length, and map them to a finite codomain such that it should be nearly impossible to find two inputs that go to the same place (although they necessarily exist) and should also be nearly impossible to find the input that corresponds to a given output. You should look up the algorithm (it is public knowledge I believe since knowing the algorithm won't necessarily help produce an attack) and try to figure out how it works. If you figure it out, teach me, because I don't know!

I will edit and add more if I think of them, but these are the ones that were on the top of my head. For me personally, I was never hell bent on application and I chose to study very pure and abstract math. Choosing to pursue math, I didn't know what or how it would benefit me in life. I did it because I liked it, and I always trusted that it would be beneficial. I feel it has, and I am very proud of my mathematical abilities and feel that I am a better problem solver than most people around me, even regarding topics very far removed from mathematics. To question 'why learn math, I don't see why it is useful' is similar, I think, to asking `why go to college? I can learn all of this on my own', or 'why pay car insurance, I am not going to get in a wreck'. If you like it, keep going. It tends to pop up everywhere.

Answer 4

As we don't know much about you, such as what sort of mathematical knowledge you currently have, the particular areas you're most & least interested in, what sorts of things can most help to motivate you, etc., I believe it might be hard for anybody here to give you much specific advice. Instead, more generally, I suggest you do some research yourself. For example, I just did a Bing search on

math applied to every day problems

to find several apparently fairly good pages, such as Algebra in Everyday Life, Practical Applications of Mathematics in Everyday Life and What use is maths in everyday life?. Note these all provide fairly basic uses, so perhaps they don't show enough about how to use more advanced math for you, especially in the computer field. If so, you can adjust the search terms accordingly to help you find more appropriate Web pages.

I also suggest you check the math books in bookstores and/or libraries. Some of the books may have sections, perhaps even the most of the book, which describes how math can be used in "real" life.

In general, I believe the best way to learn is by doing rather than by more passively listening or reading. If you read about a use of math which intrigues you, consider what & how the math is being applied, including even creating your own problems that you solve. This might also help you to appreciate more about how math can be used.

As somebody who has a CS degree & now over $30$ years of experience programming computers, I believe that my math background has helped me a lot, even though much of it indirectly. However, if anything, you will likely require more math now than when I started due to things like the current important fields of AI & block chain (with AI not being used much & block chain not even existing when I was in school) involving math techniques. Also, computers are generally much faster & more powerful than when I studied programming so their uses have expanded, often involving more complex programming (plus often, either implicitly or explicitly, associated math). Although much of this complexity is often hidden behind higher level programming languages, libraries, etc., I believe it helps to have a reasonably good understanding of what they're doing if you wish to use them appropriately (and, conversely, avoid using them inappropriately). Note I am currently working on switching from mostly C/C++ Windows business programming to the AI field, but have found I struggle somewhat with the math aspects as it's been so long since I've studied or used it. However, I believe that since I have done it once before, it's still much easier than trying to learn it from scratch now.

If you find something which is of particular interest to you, that you wish to explore further but are having trouble getting appropriate details, then asking here may help get you what you're looking for.