December 22nd is celebrated as National Mathematics Day in honor of eminent mathematician Srinivasa Ramanujan,the man who believed that the subject is something divine experience for him, as he famously said, "An equation is nothing to me unless it expresses a though of God".
Everyone of us have friends who fear mathematics to death and it may also be you who have fear of math in your nerves,So, today, on National Mathematics Day, let us know some of the toughest math concepts.
The problem with Eigen vectors and Eigenvalues is not it's difficulty,but the sheer annoyance of solving a problems that run up to 4 to 6 pages, carefully checking for mistakes, because even if you bungle one small sign in the solution, you'll still get a wrong answer and you'll loose marks, and if that isn't annoying then we don't know what is. All your effort in the exam gone to waste, with the worst thing being that you still believe you got the right answer until the results show up.
Differential Equations:
It can be easier if you can remember all the differential equation forms and how to solve them,but that can be a pain to remember as it often leads to many mistakes as one solution is used for another form of DE.
Triple Integration:
Every engineering student has gone through the trouble of studying for the M1 exam, and perhaps the toughest nail to hit in that subject, has to be triple integration. It's not that it's difficult to learn, but it is very difficult to master as the multiple integrals in the question can sometimes throw you off your calculations, and perhaps the biggest problem with this topic is that you keep doubting yourself, and the self doubt leads to more mistakes than you had previously made.
Probability Theory:
professor once describe probability as an easy topic to learn, which people seem to have trouble with, we bet he wasn't really popular with the students. That being said, according to Wikipedia, Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. It is not possible to predict precisely results of random events. However, if a sequence of individual events, such as coin flipping or the roll of dice, is influenced by other factors, such as friction, it will exhibit certain patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem.
It's applications are various, from predicting the weather, to predicting statistics, even predicting the outcomes of card games, to cyber security and cryptography.
Fourier Transforms:
Fourier Transforms decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the amplitude (or loudness) of its constituent notes, and no, we made neither head nor tail of what that means. Very few engineering students decide to study this while in college, and only the brave or the reckless dare touch this topic the night before the exam. It's applications include analysis of differential equations and Quantum Mechanics, so if you are interested in these fields, all we can say is, if it was easy, it wouldn't be worth it.
The subject has also humbled us and awed us at the sheer brilliance of Srinivasa Ramanujan, the Man Who Knew Infinity, who made Mathematics look easy. Happy National Mathematics Day!
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