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I have begun self-studying to refresh my college math skills and wondered if anyone can shed light on its difficulty and maybe give some tips for improvement. After several years in college, I eventually passed math courses through Calc III, but frequently had to re-take the courses to pass. Half the courses I got A's and B's the first time through, but some of them I had to re-take two or three times. My GRE Q score was pretty low 30 years ago (after passing Calc III with an A). I suspect it was generally a lack of concentration for one reason or another - not necessarily subject difficulty. I imagine some of you had similar experiences.
I am starting my review with Algebra through Calculus and preparing for Linear Algebra and then junior/senior level math subjects. If (a big if) I try to take classes, I will be hoping for all A's, so my goal is math "mastery". Maybe a high Q score on the new GRE. Any ideas on how to achieve that? Specific study techniques or tutorial sources or free e-books? Maybe a critical course on math reasoning or some such? is there a magic bullet or is it just hard work? thanks.
Last edited by highplainsrus; 10-16-2020 at 10:08 PM..
I can't help asking, OP: why? Is this for personal satisfaction, or in preparation for professional development, or a return to college for grad school?
Math classes would require a lot of work for most people. If you took the classes 30 years ago and only went to Calculus III, you would probably need to start back up at the level of Pre-Calculus or lower. Linear Algebra isn't hard, but you are likely to forget the details if you aren't using it. Are you prepping back thinking of a career in Data Science or something? I'm thinking if you were younger and required 2-3 times for some courses, then the junior and senior math courses are not your cup of tea. I don't think most of these subjects are on the GRE, and people can be admitted to highly ranked name programs in technical subjects without taking the GRE.
My observation is that for most people, math is either easy or impossible.
I am an engineer with a MSEE. For me, math courses were easy. I took every one offered in my curriculum because I knew I would get all As.
But my brother just could not do math. He started in engineering and failed calculous 3 times. It didn't matter how hard he tried. He just couldn't get it.
So I advised him to switch majors. That worked. He eventually earned a PhD in Pharmacy and ended up as editor of a medical journal.
For too many majors, math is an unnecessarily difficult requirement. I remember helping my wife, who is an RN do simple algebra. It was extremely difficult for her but she did pass. Her instructor wondered why she always got 100% on her homework problems but could barely pass her exams.
I can't think of any reason why a nurse would need to be able to solve algebra problems.
I can't help asking, OP: why? Is this for personal satisfaction, or in preparation for professional development, or a return to college for grad school?
Personal satisfaction and a possible return to grad school (14 years ago). I am applying and being accepted for "graduate post-Bacc non-degree-seeking" studies. I am looking specifically at online-only classes. I will see how I do in the undergrad subjects before deciding on a graduate degree plan. Since I am retired, the only possible professional development I am considering is tutoring Mathematics, so I am interested in both student and teacher sides of math learning.
Actually, a graduate degree is not as interesting to me as would be some kind of Mathematics Certificate. I am seeing them offered in England, but not so much in America. That program would be directed toward professionals and other graduates who feel the need for both introductory and advanced classes, but not research papers and graduate program credentials. Teachers sometimes do this to pick up a new skill and opportunities in their field.
Last edited by highplainsrus; 10-17-2020 at 08:42 AM..
Math classes would require a lot of work for most people. If you took the classes 30 years ago and only went to Calculus III, you would probably need to start back up at the level of Pre-Calculus or lower. Linear Algebra isn't hard, but you are likely to forget the details if you aren't using it. Are you prepping back thinking of a career in Data Science or something? I'm thinking if you were younger and required 2-3 times for some courses, then the junior and senior math courses are not your cup of tea. I don't think most of these subjects are on the GRE, and people can be admitted to highly ranked name programs in technical subjects without taking the GRE.
I am looking into the GRE test and it appears to only require Algebra, Geometry and "data analysis". The prep resources seem to be very good, so I am downloading those.
I like the pre-calculus re-entry point. My old math classes were taken as a young and mid-life student with lots of life distractions and interruptions. Math studies demand consistent, sequential progress with fresh memory at each stage.
I am trying to read Linear algebra e-texts and find it a dense subject that is understandable and readable in some texts. Their approaches to the subject vary, but brushing up on algebraic concepts and operations is certainly necessary. My math classes ended when I tried Differential Equations and stumbled badly.
Last edited by highplainsrus; 10-17-2020 at 08:45 AM..
My observation is that for most people, math is either easy or impossible.
I am an engineer with a MSEE. For me, math courses were easy. I took every one offered in my curriculum because I knew I would get all As.
But my brother just could not do math. He started in engineering and failed calculous 3 times. It didn't matter how hard he tried. He just couldn't get it.
So I advised him to switch majors. That worked. He eventually earned a PhD in Pharmacy and ended up as editor of a medical journal.
For too many majors, math is an unnecessarily difficult requirement. I remember helping my wife, who is an RN do simple algebra. It was extremely difficult for her but she did pass. Her instructor wondered why she always got 100% on her homework problems but could barely pass her exams.
I can't think of any reason why a nurse would need to be able to solve algebra problems.
I tried the switching majors approach into business and information systems. That got me into a reasonably successful career. Programming came easy to me. Now I am attracted to math as a pure intellectual pursuit, especially as it relates to philosophy - a subject I am also self-studying. I'm kind of approaching both subjects from high and low levels to see how best to study them. My tentative direction is toward philosophy of mathematics, so a solid grasp of the fundamentals is important.
Since you found math easy, did you find the textbooks also easy to understand? I tend to read slowly, with lots of visualization of the formulas, graphs, and shapes. The problems as worded are sometimes unclear and puzzling, with non-intuitive solutions. I remember encountering actual errors in the texts that would hang me up until I consulted other texts for clarification. Pencil and paper are critical, as are notes to reinforce and interpret the texts. Have you thought much about why you found math easy?
As I explore various sources, it looks like this thread could have been simply titled "mathematics education".
As a high school student (and female) I was placed in some higher math classes until my brain would not compute haha.
I too need to see things mentally to understand them and my eventual calling was in visual arts.
Retired from a photography career now I am an abstract painter who self-taught myself carpentry skills and make 3 dimensional polygonal shapes in wood to paint. Heavy on angles and requiring similar visualization. My brain is now able to handle things it could not at a younger age.
The more you go into a math area you have an interest in the more your brain opens up to absorb it.
Perhaps you need to specialize in those math areas you have a proclivity for, not be an all-rounder in other words.
We have a Daughter-In-Law who is a brilliant Attorney but cannot calculate the tip for a Restaurant tab. Go figure....
Personally I think she convinced herself decades ago that she can't do math.
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