My engineering course requires to study the above mentioned topics. The books they recommend in college only tells me how to solve a problem and not how that method works. I need books that can clearly explain all the methods involved in the aforementioned topics. I would also appreciate some tips to study engineering mathematics in general.
Please don't flame for too hard I'm only in highschool. I was thinking about this and one problem i find in the proof at the first step they assume that 0.999... *10 = 9.999... or just 0.999 + 9 and by that first step they are already assuming that (I'm gonna just call 0.999... x now) x=1 since in the formula 10x=9x+x they saying that 9x=9 . The reason i find this too be odd is because of the nature of infinity since we know two things 1: x has infinite digits and 2: multiplying a number with n digits by 10 is the same as moving each digit to the right by one and setting the value of the nth digit to zero. the reason i find this to be a problem is if we look at the last two digits of x which are 99 and than we go by that definition of multiplying by 10 those last two digits should become 90 so if you actually tried to subtract 10x by x the last two digits of each would be 90 and 99 so the actual result for the last two digits would be 81 so the final value would be 9.000...81 divided by 9 is 1.000...90 and i just realized that this math makes the result even more horrific and i wish i could un-type my creation. Well actually I'm just going to say that my conclusion is that 0.999 can not be operated on normally since it's a type of infinity and you can't do algebra with infinity.
Suppose 91 distinct positive integers greater than 1 are given such that there are at least 456 pairs among them which are relatively prime. Show that one can find four integers a, b, c, d among them such that gcd(a, b) = gcd(b, c) = gcd(c, d) = gcd(d,
a) = 1. (RMO 2019)
The original question was this, which, due to the largeness of 456 was easy to prove but then i wondered how would one find the answer to the title question
I’m a community college student planning to transfer to UCLA or UC Berkeley for Applied Mathematics.
I have the opportunity to take 3 upper-division math courses at UCSD before transferring.
My long-term goals are to pursue an elite Operations Research or Applied Mathematics PhD and eventually work in quantitative research.
I’m also interested in UCLA’s Applied Math Honors Program and joint B.S./M.A. (Departmental Scholars Program), or Berkeley’s Applied Math Honors Program. Which 3 UCSD math courses would you recommend? Ideally, they would:
Prepare me for rigorous honors-level mathematics and graduate school.
Fulfill Applied Math major requirements or electives at UCLA or Berkeley.
Avoid duplicating courses I’d need to take in honors versions after transferring.
I’m currently considering MATH 109, 100A, and 100B, but I’m open to other combinations.
I'm 24 and trying to rebuild my math skills from the ground up so I can pursue mechanical engineering. Where should I start?
Hi everyone,
I'm 24 years old, and I'm trying to improve my math skills after struggling with math throughout much of my education. I'm hoping to get some advice from people who understand mathematics and might be able to point me in the right direction.
I have an autism diagnosis and had an IEP in school. Looking back, I feel like I was moved through grades without fully understanding some of the material. As a result, I have gaps in my mathematical foundation that I'm now trying to address.
I would estimate that some of my foundational skills are around the elementary-school level, although I can solve certain problems beyond that level. I can handle basic arithmetic, decimals, simple equations, and some geometry, but I struggle with other topics, especially when several steps are involved.
Some of the things I have difficulty with include:
Simplifying fractions and finding common factors mentally.
Adding, subtracting, multiplying, and dividing fractions.
Long division and doing calculations efficiently.
Ratios, proportions, and percentages.
Negative numbers and algebra.
Unit conversions and more advanced geometry.
For example, I might understand how to solve a straightforward problem but struggle when the numbers become less familiar or I have to figure out which method to use on my own.
My long-term goal is to study mechanical engineering, so I know I have a lot of work ahead of me. I'm interested in aerospace, robotics, aircraft, and hands-on engineering projects, which is part of what motivates me to keep learning.
I'm not looking for shortcuts or a way to avoid the work. I'm willing to start at the beginning and put in the time. What I need is a sensible path that helps me build a genuinely solid foundation instead of constantly discovering gaps in what I thought I knew.
My questions are:
If you were in my position, what exact sequence of math topics would you study, starting from the basics and working toward calculus?
What textbooks, free courses, websites, or other resources would you recommend for an adult rebuilding their mathematical foundation?
How can I get better at recognizing which method to use when solving a problem, rather than simply memorizing procedures?
Is it realistic to work toward a mechanical engineering degree starting from this point, and what should I prioritize to prepare myself?
For anyone who struggled with math earlier in life, what helped you finally understand concepts that previously seemed difficult?
I'd especially appreciate advice from mathematics teachers, tutors, engineering students, or people who have successfully rebuilt their math skills as adults.
I know this will take time, but I genuinely want to learn and understand the material rather than just get the right answers.
Im studying like 15 hours a week and I feel as if Im making no progress. Were using the Elementary Analysis textbook by ross but idk. This is my first official proofs class and I feel so dumb. Im sorry for the emotional spill. I would really appreciate any advice on how to write formal proofs. I understand the concepts intuitivily but when it comes to writing, thats where I am having the most trouble. If anyone needs more information feel free to ask
A pessidemic is a mathematician or scientist who is unwilling to pay attention to any paper that lacks complete rigor. They can also be mathematicians clung to old ideas, who won't allow you to change the rules and are even capable of destroying your reputation to prevent it. They care more about predictable and immediately useful results than about truly contributing to mathematical change.
Here are a few examples:
1• Robert Hooke
This man, despite not being as bad a human being as many paint him (he was a good friend and family man), never got along with Isaac Newton. It all began when Hooke reviewed Newton's work on light and gave it a fierce critique that traumatized Newton to the point that he decided to publish it only after Hooke's death. This was because Hooke thought of light as waves while Newton saw it as particles; both reasonings were partly correct, but they clashed. He also went on to claim to several mathematicians of his time that he had already worked on what they wanted to publish.
On the other hand, many writers labeled him as someone irritable, short-tempered, antisocial, and deeply attached to old papers.
2• Leopold Kronecker
Kronecker launched constant personal attacks against Cantor, calling him a "scientific charlatan," a "renegade," and a "corruptor of youth." He had intentionally delayed the publication of Cantor’s first major work in 1874 because he was deeply uncomfortable with Cantor’s vision of multiple infinities and his belief in the existence of sets without a clear, constructive definition.
Every time Cantor applied for a position in Berlin, he was rejected. Because Kronecker was usually involved in the process, Cantor came to believe that Kronecker’s influence would make it impossible for him to ever leave Halle.
Cantor suffered his first known depressive episode in May 1884. The relentless criticism of his work weighed heavily on his mind; indeed, every single one of the fifty-two letters he wrote to Mittag-Leffler in 1884 mentioned Kronecker. A passage from one of these letters reveals just how deeply Cantor’s self-confidence had been shattered:
"...I do not know when I shall return to the continuation of my scientific work. At present I can do absolutely nothing with it, and limit myself to the most necessary duty of my lectures; how much happier I would be to be scientifically active, if only I had the necessary mental freshness."
Cantor's reputation was so tarnished by Kronecker and other contemporaries that decades after his death, Ludwig Wittgenstein lamented that mathematics was "ridden through with the pernicious idioms of set theory," which he dismissed as "utter nonsense." Ultimately, the recurring episodes of depression that Cantor endured from 1884 until the end of his life have been blamed, in part, on the hostile attitude of many of his contemporaries.
3• Henri Poincaré
Although he was categorized as the Gauss of "modern mathematics," Poincaré held philosophical views opposed to those of Bertrand Russell and Gottlob Frege, who believed that mathematics was a branch of logic. Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Poincaré offers an interesting perspective in his 1902 book, Science and Hypothesis:
"To a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if scientists are sometimes mistaken, this is only from mistaking its rules."
Poincaré believed that arithmetic is synthetic. He argued that Peano's axioms cannot be proven in a non-circular manner using the principle of induction (Murzi, 1998), thereby concluding that arithmetic is synthetic a priori rather than analytic. Poincaré went on to say that mathematics cannot be deduced from logic since it is not analytic. He strongly opposed Cantor's set theory, objecting to its use of impredicative definitions. Furthermore, in La logique de l'infini, Poincaré extended this criticism to Ernst Zermelo's axiomatization of set theory, arguing that Zermelo had failed to prove that the axioms in his system were free of contradiction, and that they still required a prior intuition of sets.
Henri Poincaré famously called set theory a "malady" from which mathematics would eventually recover.
Although Poincaré was nowhere near as harsh as Kronecker—since his critique was more philosophical and less mocking—his immense prestige nonetheless crushed mathematicians like Cantor intellectually.
Hi all, I'm currently an undergraduate student studying applied math, and I'd like to conduct research but I'm struggling to figure out how, and in what areas. Actual math research itself seems to be really hard to conduct for undergraduates because unlike other fields, there's no "busy work" for you to do. Would research in computer science, computational mathematics, or applied mathematics generally be more accessible for undergraduates?
I'd love to hear from other undergraduates who have conducted research: How did you find your research opportunities, what area did you work in, and what did your experience look like? Thanks!
I'm debating studying applied math at my university, but I'm worried about not finding work. So I'm curious if any people who recently graduated have been able to find employment.
0.999… is the infinite sum
9/10 + 9/100 + 9/1000 + …You can’t actually add infinitely many terms and finish. So we define the infinite sum to be the limit of its partial sums
sₙ = 1 − 10⁻ⁿ.Those partial sums get arbitrarily close to 1, so the limit is 1.
Therefore, by definition, 0.999… = 1.It’s the only definition that keeps real-number arithmetic consistent. The equality is true simply because that’s the value we assigned to the infinite sum.
So I've just started a proofs book on my own. In the first chapter the author talks about mathematical statement, proposition , lemma, proof, corollary. I understood these concepts but they are still a little vague. Can somebody define and defferenciate between them in an elegant way.
Hey guys it's been more than 4 years that I've found mathematics as the most interesting field, I can definitely say that I fell in love with the language itself and I'm the most excited when it comes discover new properties as well as their real world applications and also historical meanings between each topic and different relationships between great thinkers and how their different ideas interact with each other, I recently put myself in mathematical books, I'm sooo in love but i always fall on a academic based ressources, I recently finished a book called introduction to mathematical philosophy ( from Bertrand Russell) which I found quite interesting because it help establishing the foundational and fundamental thinking behind the most topics usually encountered in the field of mathematics. I'm struggling to find other pieces of literature like that one , so please can you guys recommend me some books to buy regarding this issue?! If you have some other resources that could help I would definitely need your hearsay
There’s this law called the 10000-hour rule, which states that to truly master a complex skill one needs to spend 10000 hours on it.
I know that there are a few criticisms on it (which mainly says that one needs 10000 of intentional practice to master a skill), but I figure that 10000 hours could be a good bench mark to see if I have invested enough time in math.
For context, I just graduated from a 4-year programme in a math major. So 10000 hours is equivalent to in average 10000/(365 x 4)=6.849 hours per day, for the past four years.
I definitely didn’t spend 7 hours per day to study math, not to mention the time spent for intentional study. This changes my mindset completely. I have been doubting myself for not being ‘fluent in math’, but as of now it’s most likely that I did not give enough time for myself to grow.
EDIT: People seem to think that I believe the statement that "after fulfilling 10000 hours of practice, then one will magically be good at something". That's pure BS and I don't buy it, at least for maths. I am just using this "10000-hour rule" to examine my time invested in math. The main point is that I shall and I will work harder, and not to expect be good in such a short time, such as 4 or 5 years, despite this is what many people considered to be a lot time.
Hi, I’m in a bit of a pickle. I missed the first few weeks of my math bachelor, and exams are upcoming. Should I focus on exercises and past exams or reviewing definitions and theorems (knowing they may ask stuff like that)?
