Why is linear algebra so hard

EDIT: Thank you to the people who replied. Mathematicians are chronically lost and confused. It's our natural state of being, and it's okay to keep going and take what insights you can. I suggest you don't worry too much about verifying every claim and doing every exercise before moving on. If it takes you more than 5 or 10 minutes to verify a "trivial" claim in the text, then you can accept it and move on.

It's healthy, if you get stuck on such a problem, to think about other problems or come back to them later. It's not uncommon to find that by the time you revisit them you've literally grown so much mathematically that they're trivial.

This needs to be emphasized more in learning maths. Once I got over this fact and was guided by my interest rather than wanting to grok everything, I actually started understanding a lot more. Someone should tell us that sooner then. I've been trying to get over math anxiety for a long time, and having professors that say "it's simple, what don't you understand? A common joke among mathematicians.

Two mathematicians are working on a problem and one makes a claim to which the other replies, "That's trivial! The other says, "Is it trivial? I started reading it for a class but I wasn't assigned all the problems. Later, I managed to propel myself through it by building confidence with the problems of the first few chapters which were easy by that point and then embracing the sunk-cost fallacy to get through the rest.

One problem stood out. I forget the chapter, but I'll never forget the problem: prove that normed vector spaces are inner product spaces IFF the parallelogram law holds. That's not a strategy. The first paragraph was my strategy.

My only point here is that you aren't alone in getting stuck. I actually skimmed the book over before I took my first course in linear algebra doing some of the exercises on my own, but certainly not all--I skipped anything that seemed too hard or just too boring during this reading.

At that point, there were definitely parts of the book that were challenging to me, and I just jumped over them. Then when I took the actual course, I more or less ignored the main course textbook and instead tried to tie whatever happened in the last lecture with what I found in Axler.

I considered Axler my secret weapon. It honestly felt like I had access to secret insights that trivialized the class and granted me the same intuition the professor had. I agree. I am also working through this book and feel the same as you. I think also part of the problem maybe not being able to discuss this with other people. I'm trying very hard to get through it but I think I miss being able to discuss problems with other students in a traditional classroom setting.

These sorts of discusses can really help clarify things rather than just staring at the page for a long time. A side note: how do you feel when you've lost your motivation? Is it common to barely be able to keep your eyes open?

Or is that just me! It's not just you. It's probably easier to accept that I'm sleepy and should take a rest, than to acknowledge that I need to focus and think harder about the material. Not just you. I'm procrastinating on one of those too-damn-hard math problems right now! Linear algebra is about vector spaces; matrices are a separate topic. BTW, it's written by a physicist, not a mathematician. No, he defines the determinant as the product of the eigenvalues, and this is almost the entire point for his writing the book!

This book treats linear algebra like any other mature mathematical subject. It just so happens that it's easier to understand than most mature mathematical subjects. But yeah this is just how any pure mathematician would approach the subject which is why I liked it so much. That particular series contains some of the best math texts I've read. The books are very aptly priced and are extremely well written. What is the equivalent book for other topics in math I'm trying to self study e.

Calculus, Abstract Algebra, Probability, Statistics? Any idea how this compares to Hoffman-Kunze? I liked Hoffman-Kunze because, despite being dense, its no-nonsense and very rigorous. I do so agree. Axler's book is also by far the most Geometric book on Linear algebra that I've ever read. Pitarou on March 3, prev next [—]. Nice title. I'm hoping for a Math textbook written like its an abusive drill sergeant. We're still just laying the mothafuckin groundwork, you halfwit.

This math is not hard. This math is easy. And I'm gonna make you bust your brain against these exercises until you make it look easy. Now pick up that goddam pencil and WORK your brain. I'm glad I didn't take the Math courses you went through : Perhaps, that's why I like it so much. Pitarou on March 3, root parent next [—].

That's because you're a pussy. It is the study of change in functions and their derivatives using a limiting process. It is the mathematical branch that uses small increments or decrements with particular reference to the rate of growth to arrive at solutions to a wide range of problems in science and technology.

Calculus is further divided into. If you ever want to read it again as many times as you want, here is a downloadable PDF to explore more. Algebra and Calculus are closely related as much as one has to constantly use algebra while doing calculus.

Being familiar with algebra, makes one feel comfortable with calculus. Algebra will let you grasp topics in calculus better and vice versa.

But we can also do an analysis of algebra vs calculus. To conclude, though there are many points for Algebra vs Calculus, Algebra and Calculus like everything in mathematics have a synergy and are used together in solving problems. Linear algebra is the study of the properties of vector spaces and matrices. Calculus and linear algebra are fundamental to virtually all of higher mathematics and its applications in the natural, social, and management sciences.

These topics, therefore, form the core of the basic requirements in mathematics both for mathematics majors and for students of science and engineering. The derivatives can take you from velocity to acceleration, but to visualize its practical application you need to learn physics and computer science, etc.

The concepts of linear algebra are extremely useful in physics, economics, social and natural sciences, and engineering. Linear algebra is called linear because it is the study of straight lines. It is the mathematics for solving systems modeled with multiple linear functions. Many systems in nature can be described by multiple linear equations. Being easy to solve, every area of modern science contains models where equations are approximated to linear equations.

In Multivariable Calculus, we study functions of two or more independent variables e. Multivariable Calculus expands on your knowledge of single variable calculus and applies to the 3D world. In other words, we will be exploring the functions of two variables which are described in the three-dimensional coordinate system. To conclude, although llinear algebra vs multivariable calculus display different difficulty levels their interdependence and contributions to science and technology can't be ruled out.

As the name goes by, linear algebra is the study of straight lines involving linear equations. Calculus is about understanding smoothly changing things involving derivatives, integrals, vectors, matrices, and parametric curves, etc. The following mentions the level of difficulty of the question is linear algebra harder than calculus. Similarly considering area and volume, Linear algebra deals with areas of perfect circles and volumes of regularly shaped solids, while calculus is used to find enclosed areas with curved borders and volumes of irregularly shaped solids.

While the former uses simple quadratic equations, the latter uses equations with higher exponents which are certainly harder than the simple quadratic equations.

Hence a subject difficult for someone could be easy for some other. There will certainly be a difference of opinion. The debate over which is more difficult - algebra or calculus is a classic one. It will go on forever. However, let us summarise their broad similarities and differences here. Algebra and Calculus though belong to different branches of math, they are inseparably related to each other.

Looking into algebra vs calculus, applying basic algebraic formulas and equations, we can find solutions to many of our day-to-day problems. In fact, a good understanding of algebra helps one master calculus better.

Both linear algebra and calculus involve determining length, area, and volume. As for determining length, Linear algebra deals with straight lines involving linear equations, whereas calculus may calculate the length of curved lines involving nonlinear equations with exponents. Which path a person chooses to reach to his answer depends upon his mathematical thinking.

Multivariable Calculus is considered the hardest mathematics course. Calculus is the hardest mathematics subject and only a small percentage of students reach Calculus in high school or anywhere else. However, as with all other disciplines, the choice which is more difficult finally depends upon the interest and aptitude of the person pursuing it. Another thing to consider is the department that you take it in. If you take it with the computer science department then it will likely be much more computational in nature.

Whereas, if you take linear algebra within the math department then it will make it more likely that it will be slightly more abstract and you might find that they ask more proofs on the exams. There are a number of things that you can do to make linear algebra go much more smoothly that I will mention below. It would be helpful to plan the semester out as soon as you get the syllabus for each class. In linear algebra and most other math classes there tends to be a reasonably high weighting on the homework.

However, many students do not take it so seriously. This is a big mistake. By making sure to do well on the homework you will be able to bump your grade up, make up for poor exams and you will be able to do better on the exams.

Often, students will jump straight to the homework problems before reading the chapter from the book. The problem with doing this is that the professor might have skipped on parts of the book and the questions will be based on what is in the book. It would be helpful to get help when you really get stuck. By doing so you will be able to show the professor that you are putting an effort into the class, avoid having gaps in your knowledge during the exam and you will be able to have a higher homework grade.

With that being said, it is also important to try to find the solution yourself beforehand. Otherwise, the professor will likely not be pleased and you will still struggle to understand what the professor is explaining to you. Before taking the exam make sure to prioritize any notes given to you by the professor especially if the professor gives you a study guide.

If you are concerned that linear algebra will be difficult then one option you have is to prepare for the class in advance.