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What is the hardest/easiest college math basic?

What is the hardest easiest college math basic

What is the hardest/easiest college math basic?

The easiest would be Contemporary Mathematics. This is usually a survey class taken by students not majoring in science. The hardest is usually thought to be Calculus I. This full-on, trigonometry-based calculus course is intended for science and engineering majors.

What is the hardest type of math?

This image will answer your question.

Do you see those concepts after the genius-level gap? Yeah, those concepts. They are the hardest ones out there. As you dive deeper into the mathematical ocean, it gets pitch black, and you reach the mathematical capacity of the human brain. Suppose you are a maths dude aiming to dive that deep; then best of luck. The Octopus would be there to ask you, “Bro, are you nuts? What bring them here?”

As for me, I am still at the bottom of the beginner level, occasionally doing serious maths as well. Hope will meet Octopus soon.

When I first saw Ito-calculus, I was amazed. It seemed so complicated! I tried reading books about stochastic integration but barely understood one of five sentences….

I kept at it, watched videos, read papers, and, most importantly, used it. Now, I can read papers involving stochastic integration and understand them just fine.

The point of this story is to illustrate my answer: The hardest kind of math is the kind you’ve never seen before.

What is the hardest type of math?

I would say that there is a level in mathematics called the “Genius-Level Gap,” which separates already extremely difficult math from genius-level one.

After the gap, there are some concepts that I would have difficulty grasping in an entire lifetime, and only a few people can deal with them.

I’m talking about Homological Mirror Symmetry, Complex Kleinian Groups, Perfectoid Spaces, Fermat’s Last Theorem, Poincaré Conjecture, etc.

The proof behind this is the results of years and years of research involving the best minds on earth.

Maxim Kontsevich, the man behind the Homological Mirror Symmetry conjecture.

When I first saw Ito-calculus, I was amazed. It seemed so complicated! I tried reading books about stochastic integration but barely understood one of five sentences….

I kept at it, watched videos, read papers, and, most importantly, used it. Now, I can read papers involving stochastic integration and understand them just fine.

The point of this story is to illustrate my answer: The hardest kind of math is the kind you’ve never seen before.

What’s the hardest math class you have ever taken?

It was probably Modern Algebra, which I took my first year in graduate school. Our professor was Sam Payne, an exceptional algebraic geometer, and the book was Atiyah and MacDonald’s Introduction to Commutative Algebra.

Suppose your only association when you hear “algebra” is “high school algebra.” In that case, I must disabuse you of the obvious assumption that these things must be vaguely similar. Commutative algebra is less common with high school algebra than Major League Baseball has with Teeball. Rather, it is more stuff like this:

Of course, what made this course hard wasn’t that it was abstraction-heavy. I was a math major and a pretty good one. You couldn’t scare me that easily. No, what made this course hard was the pace at which it was taught. I remember walking out of the first class feeling stunned because Sam had covered most of the material I had learned in my previous abstract algebra course… in one lecture. I remember very clearly the panic and utter inadequacy that set in.

Naturally, in hindsight, I understand why Sam taught it that way—he understood perfectly well that we had all seen this material before and most likely intended that first class to be a refresher for us. That isn’t to suggest that he let up in subsequent classes. Oh no. Sam drove us hard. I spent many a night puzzling over the problem sets he assigned, working through them with a friend with a deeper algebra background than I did. (This was an enormous blow to my self-esteem for me, who worked entirely in solitude during my undergraduate years.) I greatly respect Atiyah and MacDonald’s book, but it is not for the faint of heart: a significant amount of the material you need to learn is locked in the exercises at the end of each chapter. If you persevere through this, you will gain a far deeper understanding than if this information were just served on a platter. But you pay for every insight with sweat and tears.

As you might have picked up, Modern Algebra was hard on me psychologically—although, to be fair, a large part of this was that I was having a hard time adjusting to graduate school and all of the new challenges that came with it. But I survived and came out of it a far better mathematician than I was going in, even if much of what I learned in that class took a few more years to settle down and start making total sense completely. Sam Payne managed to whip me into something resembling a decent algebraist, and I owe him a deep debt of gratitude.

Which country has the hardest mathematics in its education curriculum?

I don’t know if this is the hardest, but to give an example of how China teaches math:

This is a page from a middle school math textbook: 3D geometry.

This is a page from a high school math textbook from China:

Also, apart from AP Calculus AB/BC, students in China cannot use a calculator whatsoever!

(Thank God I didn’t study Math in China.)

Is college math a lot harder than high school math?

Yes, it is. High school math, for me, was always very easy. It required little proof and consisted mainly of computation. To get a good grade on a test, someone had to memorize the right formulas and use them at the right time (this was even true for calculus and multivariable calculus in high school). However, I focused more on understanding the material when I went to college. The tests were now not just “apply X formula to Y,” but “You know X knowledge, now apply it to a completely new problem that you haven’t seen before.” This next step is what many students in college struggle with, as many coasted through high school, never learning how to think for themselves.

Why is mathematics so hard?

I will say “Algebraic Addition,” which adds any pair of real numbers together. This includes subtraction and subtracting a larger value from a smaller value. One example would be 321 – 767.

These operations require the basics of Addition and subtraction used since early elementary school but need a couple more “rules” to follow. However, high school and college students think it is not worth the effort since they correct these problems by themselves using the previously learned method and intuition – maybe 75% of the time. But that is not good enough for a basic math operation!

After “Algebraic Addition,” I would put Prime Factorization problems as “easy” but requiring a little practice.

By the way, to add, there are two general rules, performed in either order:

  1. Look at the sign of each of the two numbers. If they are different, you will find the difference between the two absolute values. (Conversely, if the signs were the same, you would add those absolute values).
  2. Your final answer will keep the sign of the larger of the two absolute values.

We don’t have a Subtraction rule. So if you have subtraction beyond what you’ve done in elementary school (e.g., subtracting a larger value from a smaller value or subtracting from a negative value), change the problem to Addition by “adding the opposite” of the second addend and then using the Rules for Addition just discussed. For example: 321 – 767 = 321 + (-767).

With that subtraction example, you can see the signs are now different, so we’ll find the difference of 767 – 321. The answer will then have the same sign as the larger addend’s absolute value (767), which was negative. So:

321 + (-767) = -446. Seems easy? It is, but it takes some practice to get perfect!

This is such a “basic” operation that it can trip one up for all, following math to algebra to calculus if one is not well practiced.

Pre-algebra is the easiest, which covers Addition, sub, multi, div, Fractions, Whole numbers, Decimals, basic Geometry, and percent. In summary, the Math that a student would know when finishing 6th grade. ( primary school)

The most difficult is hard to identify; if a student has the required pre-requisite, they should not find a course difficult but challenging. If I had to pick one from my own experience, it would be the second calculus course for science). For those in other majors, it would be Calculus 1 for liberal arts, etc.

Why is mathematics so hard?

Originally Answered: Why is math so hard?

I’ve struggled with this my whole life. I’m one of those who gets it. But as a math teacher, I must figure out why people don’t get it. Here are some of the conclusions I’ve found through both anecdotes and looking at research.

Math is cumulative.

Students are often used to learning and dumping. Learn it, test it, forget it. Math doesn’t allow you to do this.

This is also a nightmare for students who have been absent for a long time or have a crisis, like parents who divorced, a relationship gone bad, or a long-term medical problem. Not to mention what happens if they get a horrible teacher one year. If this happens in any other subject, you can have success the following year. With math, you have to fill in those gaps before moving on, but most students don’t, and with a one-size-fits-all curriculum, it’s hard to get those gaps filled.

(As a side note: If your kid struggles in math or misses a bunch of school, I recommend intervention early rather than late.)

It is, by nature, abstract.

Math is intentionally abstract. The idea is to create abstract tools that can be used in various contexts, but this abstraction trips many people up.

When you give some people specific hands-on problems, they can solve them. When you confront these same learners with abstract ideas, they can’t see the trees for the forest. They can’t make the connection between an abstract idea and the specific scenarios in which they would apply this abstract idea.

Good teaching can get around this by building an abstract idea through a series of specific examples rather than vice versa.

Concepts are sometimes introduced at inappropriate times.

Different minds develop at different rates. Some milestones have to be reached before some concepts can be fully understood. One of the reasons that people hate fractions is that some have to learn and use them before their proportional reasoning is fully developed. People hate Algebra because they have to learn it before their abstract thinking is well-developed.

Some minds need to be equipped to do math.

Some have better spatial reasoning; some have better logical reasoning. Some have non-math-related issues like dyslexia, which can be a barrier to learning.

It’s best to avoid this kind of thinking, though, because development happens at different rates, and just because you don’t have as much ability doesn’t mean you can’t develop a lot. Just because I’ll never be an Olympic marathoner doesn’t mean I can’t increase my endurance considerably by running more.

It’s hard to do under emotional strain.

Any task is hard to do under emotional strain, but whenever you’re hyper-emotional, thinking logically is nearly impossible. This is why test anxiety is multiplied when applied to math. I also have students who just broke up with their boyfriend or girlfriend or discovered their dad has cancer. Those folks have difficulty doing logical tasks, even if they want to.

Math can’t be faked.

In liberal arts, there aren’t as many objective standards as in math.

If you don’t believe me, look at the quantity of liberal arts degrees versus the quantity of STEM degrees. STEM degrees are hard because you have to know what you’re doing, and if you don’t, it becomes immediately obvious. There are objective standards in other fields, but they are sometimes more flexible (you know it, or you don’t) as in math classes.

What should I do if I am struggling with math in college?

Make sure that you sit with maths every day. I repeat every day, at least for an hour. Every time you sit, you will know something new, however little it may seem, and slowly, it will strengthen your grip.

And, even if you can’t get on some logic, try applying it by solving some problems. It helps a lot.

And last but not least, never give up hope.

Good luck 🙂

In what order should I learn college math?

I have asked myself this question a hundred times in the past! I never realized it was the wrong but necessary question to ask.

Wrong, because mathematics is a language based on a few rules and a nonintuitive sense of order.

Necessary, because it is a part of the overall training of the brain to map the landscape of the synthesis of mathematics.

Here is my practical advice. I hope it helps you.

1. The historical development of mathematics is very different from the textbook compartmentalization of the subject. I was unfortunate not to learn from the best mathematicians at an early age. Hence, I learned it in the usual style – Linear Algebra, Calculus, Abstract Algebra, Multivariable Calculus, Commutative Algebra, Algebraic Geometry, Number theory, etc.

Do not follow this method. I sincerely mean it. That’s the first advice.

2. Now that we know what not to do. Let’s focus on what to do. First of all, solve more and read less. Yes, I repeat, Solve more and Read less. That doesn’t mean I don’t read. You begin to realize after some time that mathematics is more like digging up the hidden intuition in your own consciousness and is less about getting stuff from the outside. All of the math helps you explore ideas.

3. I met Dennis Sullivan in Paris a while ago ( one of the finest topologists) and he told me a story about his experience of meeting Misha Gromov for the first time in Paris in the 1970’s.

Dennis was a trained specialist who acquired math in the same style you are going about. He was shocked to meet a young Misha Gromov who could talk and answer questions on any subdomain of math with ease. This was beyond Dennis’ comprehension. For days, he thought of Gromov stuck in his room reading math all the time! Finally, he mustered the courage to ask Gromov, “Misha how is that you are able to tackle any topic in math with such ease”? Pat came to the answer, “Dennis, there are just 5 principles in math according to me…..”

I am trying to remember Misha’s five principles, which differ from the story’s point. The point was that Misha had been able to throw this textbook-style textbook compartmentalization of the subject into the fire and rest the whole of math on five principles that made sense to him. The story’s moral is that you should find the root of the subject for yourself. For example, one of my key principles is addition, and 90% of my number theoretic knowledge rests on my intuition of addition. The other concept is the ‘real line,” a rather abstract concept that lies at the heart of analytic, algebraic, and differential geometry, not to mention the whole of calculus.

4. Try reading many different things at once while keeping a few specific problems in mind simultaneously. So, for example, keep your target as, say, understanding the Inverse Function Theorem, The Prime Number Theorem, and The Fundamental Theorems of Ordinary Differential Equations. Be prepared that such an approach takes time to deliver results. But once you see your ability grow, nothing will stop you.

5. Try and read from the masters as far as possible. A professor of mine at the Tata Institute taught me this. I thought that this was because an idea is expressed clearly by the masters. Yes, that is true. But there is another advantage. When you read the masters, you can quickly get to the subject’s heart.

6. Try to avoid thinking and speaking to people saying, “okay I have a question in differentiation for you…” Instead, go to the heart of it and say, “Okay so I have an analytic function on such and such domain with the following properties….”

7. Be fearless and dive into the subject with nothing to lose.

Enjoy the journey, my friend. The best part lies ahead of you!

How hard is High school maths? And College/University maths?

Depending on where you live, in China, we usually do Maths for more than five hours a day just because it is so important when entering university. Here comes one page of one of my math notebooks and I have seven more, each with about 100 pages. —Don’t be surprised, we study almost 18 hours a day.

What is the hardest maths class you took in college?

As an undergrad I did economics/applied math and my grad is math/astrophysics; I’ve done a bunch of stuff in econ/math/physics, like econometrics theory/machine dynamics/advanced differential equations/signal transforms/theoretical cosmology/planetary dynamics, etc.

I attended a higher-level pure class called Logic and Set Theory as an undergrad.

The course covered the philosophy of Logic and mathematical equivalence, but part of the course was cardinality theory and choice function theory.

I was confused then, and to be honest, I’m confused now.

How do I make college mathematics interesting to study?

Here, in your case, you have two solutions:

1st) DROP OUT THE COLLEGE and choose the subject or field which you are interested in, only at your own risk.


For that, you will need the following-

Inspiration: Use the Google search engine to research and read about great mathematicians and their achievements.

Interest: Find out the applications of different topics of Mathematics and relate them to daily life. You will get amazing results.

P.S.: I did the second one while in graduation and am now pursuing my dream after getting the degree.

What college math basic do you recommend for a non-math major?

There is a backdoor if you’re a humanities type who struggles with advanced mathematics. Before you take any math classes, take a course in formal Logic.

Formal Logic is one of those easy courses many take to get out of a math course. But, it can be used as a backdoor into mathematics. I don’t have any hard data (I don’t think there have been any studies on it), but I hated mathematics until I studied Logic, at which point math somehow became easier. I have heard similar things from friends who have studied it.

I don’t know why this is, but I would guess that it relates to anxiety. A lot of people are bad at math because they “freeze up” when they see a complex formula. Formal Logic dispels that because 1) it’s easy (at the lower levels) and 2) it drives home the fact that every equation and formula can be manipulated with simple Logic. It all makes sense. It’s not magic. It’s just Logic. That makes math easier.

This will also serve you well if you decide to go into abstract mathematics. Abstract math requires proofs, which are more similar to formal Logic than high school algebra, at least, IMHO

Why do we have to take math classes in a college or a university when we aren’t math majors?

Originally Answered: Why do we have to take math classes in a college or a university when we aren’t math majors?

Three major reasons come to mind, in my experience:

  1. You use math in your major. Computer science students need applied statistics; electrical engineers need calculus; accountants need to solve systems of calculations dynamically; chemists need differential equations, etc. Anything in the STEM (Science, Tech, Engineering, and Math) usually needs lots of math.
  2. Passive skill – I’ve seen teachers need to use algebra to calculate grades, carpenters and drama instructors use geometry and trig for set building, and digital 3D artists use math for ratios in their modeling projects or helping design a university stairway. Liberal arts schools strive to make well-rounded students. At least being aware and partially skilled at a non-trade practice can make you the innovator who stands out in your field and can solve problems others haven’t seen.
  3. Critical thinking – Math teaches you how to think. Learning how to take abstract problems and dilute them into solvable bits is a trade used all the time in life. If you take the time to look up the research, you’ll find that math trains your brain more easily to solve lots of problems. Creating arguments, understanding and dissecting large bodies of literature, programming to solve a problem, figuring out the best way to move all your stuff in the fewest trips, it all comes from the part of your brain that math works out like almost no other subject.

How hard is High school maths? And College/University maths?

High School mathematics can be hard if you let it. In High School, each year is devoted to one or two (Algebra 2/Trig) specific area points. I’m aware of include Geometry, Algebra I and II, Trigonometry, Pre-Calc, Calculus, and Statistics. If you have a good instructor, ask questions when needed, review for tests, and ensure you understand and practice a concept, you will do at least C+ level work; at most, you’ll bring home A’s.

You’re just continuing to get in-depth information on each college and high school mathematics section. Each concept builds on a lesson, which builds on a course and a subject within Math. You gradually gain more information and understanding each year. To a middle schooler, math in High School and College may seem very difficult, but it is a gradual progression of understanding.

Is college math a lot harder than high school math?

It can be, but it doesn’t need to be. It also depends on what you mean by ” order; “I’m going to assume you mean “more complex topics.”If you finish high school with integral calculus (I think that’s still the upper-level AP class) and then go into a non-STEM major in college, you’ll likely not see anything new.

However, suppose you finish your high school career with a pre-calculus course and take an engineering major in college. In that case, you’ll take at least differential calculus, integral calculus, multi-variate calculus, and differential equations. You have quite a bit more if you’re going into aerospace engineering. Computer security also has field theory and the like.

And obviously, a math major mostly takes math classes, digging deeper with every course.

Why do people find mathematics difficult?

Math is difficult because everything is difficult.

Writing stories is difficult.

Dancing is difficult.

Acting is difficult.

A few years ago, I heard a section on the radio where they brought people off the street and asked them to read the weather report. They were appalling. Bad. Reading the weather on the radio takes a lot of work.

Writing good answers on Quora is difficult.

Very few people are good at any of these. But it’s hard to know how bad you are with most things. Watch the early American Idols. Most of those people are dross. But they are really, truly disappointed when they are booted off.

I could read the weather on the radio, just as well as the person who reads it now. I will be shocked to find out how bad I am at it.

Go to any restaurant or cafe in Los Angeles – most wait staff moved to LA because they wanted to be actors. They thought they could be a famous (or even working) actor. But most don’t because being a good actor is difficult. It’s

Your job is difficult. I couldn’t do it. When I tell people what my job is, they start talking to me about it because they think they have something interesting to tell me about. (II’ma psychologist.) But I have it bad. I recommend being User-13135008672097594132 – “You’re a cook. I cook in my kitchen. Let me tell you about your job.”

But if you’re not good at math, you know it. It hits you in the face. Straight away. Hard. There’s pretending or fooling yourself. I can throw a steak on a grill or make a pasta sauce and pretend I know how to cook.* But I need help to integrate that equation.

Obligatory XKCD comic:

*A friend of mine used to like baking cakes. Their friends were polite and said, “Um! Delicious cakes!””The friend thought they knew how to bake. They sold cakes to a place that did ”farmhouse Teas.’ ‘On more than one occasion, a customer returned the cake because it was inedible.

College math is hard. What should I do?

Originally Answered: College math is hard; what should I do?

Life is hard; what should I do?

Most things worthwhile are hard. Mathematics is one of them. The first step is to accept that it is hard, and this is much less trivial than it sounds. We are bombarded by easy-to-understand slogans on TV, in books, etc., and our minds reject anything that takes a while to understand.[1] This is why people hate mathematics and ”find it hard.’

‘It’s hard when you expect to understand proof in 2 minutes, like any other text you encounter daily. It’s okay if you don’t have this expectation; understand that it may take time and hard work.

Most college students go through this process of adaptation- some successfully, some not so successfully- to a new kind of learning, where one has to accept that things are hard. It’s frustrating at first, but necessary to become a mature student.

So, accept that it will indeed be harder, or at least harder than you were previously used to.

[1] In fact, these simplifying slogans make other subjects, such as politics, history, etc., seem easier than they are. As John von Neumann said, “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”

For instance, you are good at math and a math major in college. Is there any math that is considered to be the hardest?

No, for a few reasons.

  1. EEveryone’sdifferent. I find Algebra easy and Analysis hard, but some people are precisely the opposite.
  2. Every professor is different. My Algebra teacher was a joy, and my Analysis teacher seemed to deliberately make the course difficult to understand to prove his smartness. (He was a young guy teaching over the summer and might have felt he needed to prove himself.)
  3. Every department is different. The math courses at UPenn are honestly kind of a wink… except for the wildly advanced Logic courses. The Logic courses at NYU aren’t bad at all, but their Probability courses are insane.
  4. For any subject with open research questions, you can also put that question on the final, and instantly, the class becomes the hardest possible. This is a trivial demonstration that any upper-level undergraduate course is approximately infinitely hard. But it just demonstrates that, for any of these classes, what makes it hard is just a matter of which regions of the subject you choose to cover. You can stay in the kiddie pool or swim in the ocean. If you wanted to, you could make a high school Geometry class so hard that people with PhDs in Math couldn’t pass it.

There are some fields that I feel we haven’t “figured out” yet to any satisfying degree, making teaching them very hard. We have a pretty good grasp on much of Algebra and Analysis, so I think you can get good classes in those and come to understand them with only reasonable pains. However, Numerical Methods and Differential Equations … I think we need to make many more research-level discoveries in those areas before we can package those ideas in a well-organized and intelligible way to undergrads.

So, despite my “o” answer, I would also say “ut kinda” for Numerical Methods and Differential Equations. Of course, someone out there will say, “I took a course in that, and it was easy.”Again, every student, professor, and department is different. And my answer is only, “ut kinda.”

What is the hardest/easiest college math basic?

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