How can I improve my algebra so I can fully understand calculus?
December 6, 2019 12:08 PM   Subscribe

How can I improve my algebra 1 and 2 (and linear algebra) so I can feel comfortable with tackling calculus 1 + 2?

I do not have a finesse for math; I am quite slow and weak in it. Yet, I am eager to learn it and improve my algebra so I can understand calculus down the road. What are some good tips, advice, and practice guideposts to improve my algebra so I can better understand calculus? I am wanting to take some extra courses in economics and an intro to computer science to fill some university electives I need as a fourth-year undergrad student, and I thought that perhaps improving my math would be a good start. Yet, I am quite slow with math, and have struggled with taking a social statistics course in the past.
posted by RearWindow to Education (19 answers total) 27 users marked this as a favorite
 
Have you looked at Khan Academy (Algebra I, Algebra 2, Linear Algebra)? That's often what I recommend for my students who want to fill out their math background. It doesn't work for everyone, but it has been quite helpful for a number of my students.
posted by Betelgeuse at 12:20 PM on December 6, 2019 [4 favorites]


If you prefer a more traditional textbook based approach, Schaum's Outlines are a great way to learn the nuts and bolts of a variety of topics, including multiple levels of algebra.
posted by hankscorpio83 at 12:43 PM on December 6, 2019 [4 favorites]


Make sure you fully understand and can work with trigonometry, especially the trig identities.
posted by TrialByMedia at 1:00 PM on December 6, 2019 [5 favorites]


I am not in any way a math expert, but my university's math department requires that students know the concepts from Algebra I, Algebra II, and Trig before they take Calc I. So I think you should add Trig to your list. Here, Linear Algebra is an advanced math class that students take after Calc I.
posted by ArbitraryAndCapricious at 1:01 PM on December 6, 2019 [1 favorite]


I'm in the process of doing this on my own. I would highly recommend the Humongous books (Humongous Book of Algebra to start but there is one on trig too). It's nothing but problems and solutions. Do all of them. If you don't understand them, read their solution, then do it until you get it right and understand why it is the way it is. If you really don't get it, then there are lots of video sources (Khan Academy mentioned above is awesome). Some good youtubers:

Brian McLogan has a ton of videos
Eddie Woo is very good (very enthusiastic and good explainer).
Black Pen Red Pen - recommended to me but I use the two above more.

Doing problems is the key though. I am not a natural at this, but the more you do it, the better it becomes. I'm doing Trig right now, and that's less fun than Algebra. Persistence is key.
posted by mrbarky at 1:04 PM on December 6, 2019 [5 favorites]


In addition to Khan Academy, I recommend ALEKS. I'm a math professor, and we use ALEKS in some of our more self-paced classes. You can pay for modules as an independent student, and one nice feature is that it does an initial assessment which helps to highlight what you know and what you need to learn, and it feeds you work that reflects those areas.

Of course, another approach is to enroll in a course; the advantage here is that you have someone to whom you have to be accountable, so that your math study doesn't get pushed to the bottom of the priority pile, and someone who can look at your work and tell you where you have errors, and someone who can help you understand areas you are struggling with. The disadvantage, of course, is money. Lots of places, including my own institution, offer online courses, but I'm sure your university also offers face-to-face courses.
posted by leahwrenn at 1:05 PM on December 6, 2019 [3 favorites]


Seconding ALEKS. I just took this free precalculus course through EdX that uses the ALEKS system, and improved my score on a local community college placement test (administered through ALEKS) enough that I placed in to Calculus 1. We'll see when I take that class if I'm actually prepared, but regardless I really like the system, as it allows you to learn through repetition and assesses where your weak areas are.

https://www.edx.org/course/precalculus

There is also a lower level math course that is kind of pre-pre calculus on edx also through Arizona State that probably includes some algebra as well through ALEKS (I started out in those modules as it had been many years since my last math course).
posted by knownfossils at 1:17 PM on December 6, 2019 [2 favorites]


Try The Cartoon Guide to Algebra, by Larry Gonick

It's probably a thoughtful treatment, but not intimidating. Your available libraries may have it.

What are some good tips, advice, and practice guideposts to improve my algebra so I can better understand calculus?

Broadly, pay attention to when you're experiencing math anxiety where your brain is just grinding away doing negative self-talk but isn't nibbling away at the math itself.
posted by sebastienbailard at 1:30 PM on December 6, 2019


When I needed to do this, I ordered used pre-calculus textbook online and just started working through it section by section. Pre-calculus might target exactly what you need.
posted by hought20 at 1:32 PM on December 6, 2019


A kind and wise man named Herb Gross .. cannot even do justice to his teaching.. you can watch his tedx talk on the importance of teaching "Numeracy" titled "Have you Ever Seen a Number?" here -- https://www.youtube.com/watch?v=orqfXaDqm7Y

I have to say his conceptual explanation of calculus, as seen here in these timeless videos (available thanks to MIT's opencourseware), was the only time I have felt interested in calc with what I think i can actually say was something approaching rapt attention. (If you need further convincing of the genius of his conceptual approach, read the comments for these MIT opencourseware calc videos !)

Here is a playlist for his "gateways to Algebra" course: https://www.youtube.com/watch?v=Tu6HrPLGbB8&list=PL1xF7Py1h3uzsMQJ5CUTPk9TYRi7AhLr2

Professor Gross was so interested in teaching numeracy, in fact, that in '73, according to his wikipedia page, he left MIT to direct the mathematics department at Bunker Hill Community College, were he taught for the rest of his career.

Really hope folks will click through and check him out.. I think he's the bee's knees.
posted by elgee at 1:44 PM on December 6, 2019 [7 favorites]


You don't exactly need linear algebra for calculus. But I would say that I didn't really feel like I understood algebra *until* I took calculus. So do the calc and the algebra will come!

But if you want a book, this is my favorite: Gelfand's Algebra
posted by dis_integration at 1:46 PM on December 6, 2019 [1 favorite]


Another enthusiastic vote for Khan Academy's Algebra Basics program!
posted by hollisimo at 2:45 PM on December 6, 2019


Definitely Khan Academy. They divide things into nice bite sized chunks, which sometimes makes for annoying redundancy but in general means you can easily study 15 minutes here and 20 minutes there.

You’ll want to use it for calculus/linear algebra/etc also.
posted by Tell Me No Lies at 4:07 PM on December 6, 2019


I aced my college algebra course three years ago by ignoring the textbook I was assigned except for homework problems, and using instead Dugopolski’s College Algebra book and a monthly Chegg subscription. I also started with Khan Academy but I don’t learn well from listening to people talk about a subject. I found Justin Math’s videos more helpful for a lot of concepts and I like his website better. It is easier to find a specific topic. Khan Academy is great for practice problems. I liked Dugopolski’s book so much I got all of the subjects he has published.

It was the third time in ten years I attempted Algebra and had assumed I was just terrible at math. I freaking love math now even if it is difficult. I also agree about learning trig before jumping straight into calculus.
posted by apex_ at 4:43 PM on December 6, 2019 [2 favorites]


I should say, what I like about Khan Academy is their quizzes/computer-graded problems, not the videos. I am annoyed by watching videos of things where I could more quickly learn by reading (although I realize I may not be typical).

And absolutely, if you are planning on taking a calculus class that uses trigonometry, then you need to know your trigonometry before-hand. There are non-trig calculus classes (often, Business Calculus, sometimes Calculus for Life Sciences or Applied Calculus), depending on what field you are in and why you are taking calculus.

(There's also, IMHO, much more interesting, accessible mathematics out there than calculus---calculus is not the be-all and end-all of mathematics, although it is very useful in certain disciplines. But graph theory and combinatorics are super-fun; linear algebra is awesome; abstract algebra is fascinating...and none of these use calculus.)
posted by leahwrenn at 5:13 PM on December 6, 2019 [1 favorite]


As an aside, you will find out that math is a language, and like any language you need to memorize some stuff. For Algebra to progress into Analytic Calculus (as opposed to business math) you will find it eases your path to memorize the trig identities and be able to recognize them in all the variety of ways they are moved around (algebraically). Memorize, practice, memorize... diligence will pay major dividends all the way through.
posted by ptm at 5:58 PM on December 6, 2019 [2 favorites]


You you might want to look at "Calculus explained with pics and gifs"
posted by forthright at 6:19 PM on December 6, 2019 [1 favorite]


I suppose it depends on the specific course syllabus but you can take a lot of economics without having to do a lot of maths. So by all means work on your maths skills but you may not need to do that to do well in your economics class.
posted by koahiatamadl at 6:38 AM on December 7, 2019


When I taught pre-calculus our textbook was a pdf available here: http://websupport1.citytech.cuny.edu/faculty/ttradler/precalculus.html
posted by Obscure Reference at 6:56 AM on December 7, 2019


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