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Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus? This is my singular biggest hurdle
by no_wizard 3y ago
Does anyone know of an entry level book that could take someone through say, high school math to college alegbra / calculus?
This is my singular biggest hurdle in going back to school to finish my degree and I'd love to fill the gaps I have around mathematics so I can not only finish my degree; I'd also like to participate in some more advanced computer science that rely heavily on underlying computation.
- engineer_22 3y agoCheck out Kahn Academy, they have a gamified course to guide you through the equivalent of a high school and early college math curriculum. AFAIK it's free?
- engineer_22 3y agohttps://www.khanacademy.org/math https://www.khanacademy.org/math
- culi 3y agoKhan Academy is great. When I was taking AP calculus in highschool I failed to complete any homework and barely passed the class. But when it came time for the AP test I binged Khan Academy videos for 3 days beforehand and ended up getting a 5 (the max score). Great resource and even bingeable
- alphameese 3y agoSpecifically these three courses [0][1][2] will take you from basic algebra to precalc. They're very thorough and I've found them extremely useful in upgrading my high school level math skills. I have heard that their calculus courses aren't sufficient though, and that it should be learned from somewhere else. [0]https://www.khanacademy.org/math/math1 https://www.khanacademy.org/math/math1 [1]https://www.khanacademy.org/math/math2 https://www.khanacademy.org/math/math2 [2]https://www.khanacademy.org/math/math3 https://www.khanacademy.org/math/math3
- bloemheuvel1 3y agoWould you recommend this path over doing the Algebra 1 -> Geometry -> Algebra 2 …. etc path?
- alphameese 3y agoThe Math 1-3 courses intersperse all of those courses and provide a more streamlined path. I would personally recommend using those 3 courses to learn up to pre-calc.
- steppi 3y agoIt's not one book, but for everything before calculus it would be difficult to beat the books in Israel Gelfand's High School Mathematics Correspondence Curriculum [0]. These are designed for self study and give a fresh perspective on topics they cover. [0] https://www.goodreads.com/series/318605-gelfand-correspondence-program-in-mathematics https://www.goodreads.com/series/318605-gelfand-corresponden...
- wyclif 3y agoExcellent recommendation; they are very good books to start with. Concepts are clearly explained and I wish every mathematics textbook was structured like this. Some people are biased against these books because they're Soviet, but I find that attitude parochial. If we're judging textbooks on their merits alone, these will get you to Calculus.
- dataviz1000 3y agoCurious if I could find another interesting way to learn math for someone who hasn't gone to college, I asked chatGPT to cluster 20 animal emojis by taxonomy and use them to explain Affinity Propagation like I'm 5 year old. (I'm an idiot.) More or less, the lion emoji wants to be friends with the tiger emoji more than the dog emoji with some explanation of the math and math symbols in between. ``` For example, when Scar wanted to be king, he sent a "responsibility" message to the other big cats, trying to convince them that he should be the leader. However, the "availability" message he received back was weak because most animals didn't trust him. Meanwhile, Simba sent out a strong "responsibility" message showing he could be a good leader, and in return, he got a strong "availability" message back with many animals showing support. That's why Simba was a better leader for the Pride Lands, according to Affinity Propagation! ```
- ajmurmann 3y agoI love this book: https://www.goodreads.com/book/show/17406856 https://www.goodreads.com/book/show/17406856 The explanations are great and the examples and excises are such that you can just do them in your head.
- jayro 3y agoAt Math Academy (https://mathacademy.com https://mathacademy.com), we created a series of courses, Mathematical Foundations I, II, & III, that will take a student from basic arithmetic through calculus and prepare them for university-level courses like Linear Algebra, Multivariable Calculus, Probability & Statistics, etc. You can jump in at any with an adaptive diagnostic that will custom fit the course to you based on your individual strengths and weaknesses. https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-i https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-ii https://mathacademy.com/courses/mathematical-foundations-iii https://mathacademy.com/courses/mathematical-foundations-iii We also have courses on Linear Algebra and Mathematics for Machine Learning: https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/linear-algebra https://mathacademy.com/courses/mathematics-for-machine-learning https://mathacademy.com/courses/mathematics-for-machine-lear... It's not free, but our adaptive, AI-driven algorithms makes it the most efficient way to learn math that you're going to find. We've had numerous students master 3-5 years of math in a single year. We're still in beta and haven't done a proper Show HN yet, but we're getting there! I'm the founder, so I'd be happy to answer any questions.
- Gerard0 3y agoLooks great and was ready to sign up but I surely wasn't expecting that price! I am not saying it is not worth that, but as someone who has tried to start learning math on my own only to quit afterwards for whatever reason, it's a big risk to take.
- Math-Ninja 3y agoHi Gerard. Math Academy does not charge your card for the first 30 days. If you find it's not a good fit for then you can cancel within this period and you won't be charged. 30 days hopefully gives you enough time to determine whether it's a good fit or not.
- Math-Ninja 3y agoMy colleague informs me that, contrary to my previous message, you get charged immediately, but you get an automatic refund if you cancel within 30 days. Apologies for any confusion.
- diebeforei485 3y agoI found this to be a good explanation of Calculus in particular: http://lightandmatter.com/fund/ http://lightandmatter.com/fund/ It assumes you have some algebra, but does not require college algebra.
- ivansavz 3y agoI think you might like my book "No Bullshit Guide to Math & Physics"[1,2,3], which contains a condensed review of high school math (a.k.a. algebra and precalculus), then explains PHYS and CALC topics in an integrated manner. [1] website https://minireference.com/ https://minireference.com/ [2] PDF preview and sample chapter = https://minireference.com/static/excerpts/noBSmathphys_v5_preview.pdf https://minireference.com/static/excerpts/noBSmathphys_v5_pr... [3] concept map = https://minireference.com/static/conceptmaps/math_and_physics_concepts.pdf https://minireference.com/static/conceptmaps/math_and_physic... If you prefer something focussed on a review of high school math topic, then you might prefer the "green book" instead, see https://nobsmath.com/ https://nobsmath.com/
- graypegg 3y agoBought! Something in epub was exactly what I needed and loved your chill writing style in the sample chapter, cheers!
- graycat 3y agoVery fast calculus: Consider a standard car with a speedometer (reports how fast are going) and an odometer (reports how far have gone). Easily enough we can take the speedometer readings, say, 1 time each second, and calculate a good approximation to the odometer readings. That is a 1 second approximation to the calculus operation of integration. Similarly we can take the odometer readings, say, 1 time each second, and calculate a good approximation to the speedometer readings. That is a 1 second approximation to the calculus operation of differentiation. If we use smaller time intervals than just 1 second, then we will usually get a more accurate approximation. It is a theorem that, under mild assumptions, as we let the lengths of the time intervals shrink toward 0, the results of the operations will reach limits and quit changing. Those limiting values are the actual definitions of differentiation and integration. No big surprise, under mild assumptions, if we start with the odometer readings, differentiate to get the speedometer readings, and integrate to get back the odometer readings, then we really will get back the odometer readings. That is the fundamental theorem of calculus. Some common mild assumptions are basically that the speedometer readings change only continuously (no jumps) over time and we are working over only finitely long time intervals. Newton's second law of motion force = mass x acceleration essentially guarantees the continuity of the speedometer readings and, thus, justifies the integration back to the odometer readings. Of course, calculus and Newton's second law of motion are close cousins in both theory and applications -- no big surprise since Newton essentially created both (might mention Leibniz and some others). Can quickly show that if we integrate time t, we get (1/2)t^2. So if we differentiate (1/2)t^2 we will get back t. A calculus course will show how to differentiate and integrate a wide variety of mathematical expressions, polynomials, sines and cosines, products, quotients, composite expressions, etc.. E.g., differentiate sine(t) and get cosine(t). Differentiate cosine(t) and get -sine(t). Can also find many cases of arc lengths, areas, volumes. Suppose we are starting a business. At time t, let the revenue be y(t). Suppose we have argued that as we reach all our target customers, our monthly revenue will be b. Suppose we argue that due to word of mouth advertising the rate of growth is proportional to both the number of happy customers talking and the number of target customers not yet customers listening. Denote the rate of growth of y(t), that is the derivative, by y'(t). Then for some constant of proportionality we should have y'(t) = k y(t) ( b - y(t) ) Of course we know current revenue, say, at time t = 0, that is, y(0). Then by the first weeks of calculus, can show that, with TeX syntax, y(t) = { y(0) b e^{bkt} \over y(0) \big ( e^{bkt} - 1 \big ) + b } More generally y'(t) = k y(t) ( b - y(t) ) is an example of an initial value problem of a first order, linear, ordinary differential equation and an introduction to a course in ordinary differential equations. Calculus has wide applications to physical science, engineering, economics, finance, spread of diseases, etc.
- rg111 3y agoFor this partcular purpose, look no further thank Khan Academy. I recommended a lot of people these courses and myself went over a few videos to revise Trigonometry. I can vouch for the quality.
- nemexis 3y agoI absolutely adore the works of John Bird: https://www.google.com/search?tbo=p&tbm=bks&q=inauthor:%22John+Bird%22 https://www.google.com/search?tbo=p&tbm=bks&q=inauthor:%22Jo... it really takes you from the ground up all the way to advanced subjects. He published multiple books on various levels of mathematics.
- sn9 3y agoThe aops books [0] will take you from prealgebra all the way to calculus and discrete math and will give you a foundation strong enough to enter any undergraduate math program in the world. And the books all have complete solutions manuals available so you can get immediate feedback. You could use programs like Anki to schedule your review of defintions you've understood and problems you've solved to supercharge your learning as well. [0] https://artofproblemsolving.com/store https://artofproblemsolving.com/store
- melagonster 3y agotry khan academy first?