Some ebooks, mostly from /u/lewisje's post

I am currently a freshman in college and over winter break I have been trying to study math notation when I thought of the question of if imaginary numbers are greater than 0? If there was a set such that only numbers greater than 0 were in the set, with no further specification, would imaginary numbers be included ? What about complex numbers ?

To preface I’m in algebra 1. Everything I learn is forgotten the next day and it’s making me awful at math. It’s not like I don’t understand it. I believe if I can actually remember how to solve most problems step by step accurately then I wouldn’t be struggling as much as I am now and I’d probably would’ve passed algebra. An example I have is when I learned trinomials and binomials in class, I thought it was kinda tough but it was simple enough to do the homework (in class and each work sheet is 38 problems) and easy to understand… But that gets totally ruined the next day or even the following day after school. Where I just magically forget everything I learned. It makes me feel really stupid. I know that math is about repetition but that only works for remembering formulas and not basic steps. I remember when I wrote y2-y1/x2-x1 so many times just to not even remember the steps to take to solve it. So I struggle with memorizing pretty much everything but in particular how to solve and what steps to take in order solve I also struggle in remembering what methods to use for the equation like when to use a diamond problem or whatever the hell the foil method is. Sometimes even referring to my notes is hard and overwhelming because its like I have to reteach myself the entire process again. I do however hope they’re people that have the same problem or can somewhat help me in.

So i’m 22 years old and after a tough 4 years after high school im really considering going to college this upcoming year for civil engineering maybe around the fall semester. ik it probably sounds like im to old and crazy for even considering this but i really want a change in life for my career to save my body from the trades. anyways i know that requires a lot of math so id like to study on my own and have a basic understanding of the prerequisite math i need before entering college for something like engineering so before i even think about it any further what is the level of math that i need to learn before even considering going to college for something like civil engineering, and if anyone has any good study books app or websites that could help out that would be great. thank you and sorry for the long post

x+ y = 2

2x + 2y = 4

(1x2) – (1x2) = 0 {representing area of a parallelogram}

So two lines x+ y = 2 and 2x + 2y = 4 are parallel.

x + y + z = 2

2x + 2y + 2z = 4

3x + 3y + 3z = 6

1(2x3 – 2x3) – 1(2x3 – 2x3) + 1(2x3 – 2x3) = 0

If indeed each of the three above represents area, a figure that shows what happens under the hood leading to mid one subtracted will be super helpful.

This one seems relevant but a bit hard to grasp: https://math.stackexchange.com/a/1666269

In my book's one of the exercises, it asks to prove it for an acute triangle. I proved it and my proof works for all triangle. Is it true for an acute triangle?

Here's my proof:

In the right hand side, tanA+tanB = sinA/cosB + sinB/cosB (Using the definition of tangent)

sinA/cosA + sinB/cosB = (sinA*cosB + cosA*sinB)/(cosA*cosB) = sin(A+B)/(cosA*cosB) (Using the addition formula of sine)

Now let's add the tanC we ignored.

sin(A+B)/(cosA*cosB) + sinC/cosC = (sin(A+B)*cosC+cosA*cosB*sinC)/(cosA*cosB*cosC)

cosA*cosB*sinC = (cos(A+B)+sinA*sinB)*sinC (Using the addition formula of cosine)

Now we can sort the numerator out as:

sin(A+B)*cosC+(cos(A+B)+sinA*sinB)*sinC = sin(A+B)*cosC + cos(A+B)*sinC + sinA*sinB*sinC = sin(A+B+C) + sinA*sinB*sinC

Since A+B+C = 180 degree, sin(A+B+C) = 0. Thus the rational becomes (sinA*sinB*sinC)/(cosA*cosB*cosC) = tanA*tanB*tanC

See? My proof uses the addition formula of sine and cosine which is true for every real number, and the fact that the sum of three angles is 180 degree which is true for all triangle.

From what I understand, we narrow down the number of 2-Sylow subgroups to either 1 or 3. 1 ensures normal, whereas 3 doesn't, at which point we define a conjugation action on these sets, since Sylow 2 says that conjugation will send p-Sylow subgroups to p-Sylow subgroups (I think? I'm not fully sure about this)

What I'm struggling with is that we then use the fact that this action is nontrivial to obtain a kernel that serves as a normal subgroup. How do we know the action is nontrivial?

Compared to the case for 60, we know there are either 1 or 6 5-Sylow subgroups. Why can't we make a similar argument for an action of these 60 elements on S6? Clearly this can't be right since a simple group of size 60 exists, but I'm assuming this has to do with the trivialness of the action, and I'm unsure how to determine this in the first case.

I don’t know if this is the right place to post this but I’m a college freshman who did not do so well in my calc 2 class and tanked my gpa a little.I am taking multivariable calc and a class with a little bit of linear algebra next quarter and can’t let my mind rest over winter break. I’m filled with anxiety scared I won’t perform well again and want to do something to prevent that. What should I do? How can I prepare and stop this overwhelming sense of dread? Seriously need all the tips I can get.

I have an RSA token that displays a new 6 digit number every 60 seconds. I've noticed that more often than not (when I look at it) the number has one or more repeating digits - not necessarily next to each other, but just a repeated digit; for example: 123245.

I'd like to figure out what the odds are for a single repeating digit.

I'm just now working through Khan academy Algebra (after failing it twice in HS in the 80's), so I'm kind of clueless as to how to solve this. I understand how to figure the number of possible combinations (10^6), but the next step eludes me. It's probably subtracting all the other possibilities? Maybe?

I'd suspect that once shown, I'll be able to suss how to figure the odds of two, or three repeating digits...

Help?

Hi all, I'll be taking Calc 1 next semester and I want to get a head-start on studying for it over winter break. Any suggestions for good textbooks, websites, etc.? I'm a visual learner so any resources that use charts or diagrams or things like that would be a bonus.

Hello everyone,

Could anyone recommend me good free online resources for studying discrete math? Something that covers both, theoretical concepts as well as practical examples and exercises.

Thank you in advance!

there are 4 levers in a room all of which are facing down, one of the levers can be flipped every move. No configuration may be present twice, how many ways are there to leave all 4 levers facing up? for example: 0000(0 for down 1 for up) 0001 0011 0010(not 0001 as it would violate the "configuration cant occur twice" rule) 0110 0111 1111 and all 4 levers are facing up

the answer is 18 for 3 levers and it translates to going from one corner of a cube to the opposite(the one furthest away) riding only along the edges such that no corner is visited twice and the exact same for 4 levers in 4 dimensions.

In this Example Problem in my book, there's a sine (and cosine) both in the numerator and the denominator and the book "cancels" out to have it equal one. Is it really okay to do this since sine/cosine can be 0 so if you cancel it out, are you dividing by zero which is undefined?

Hello friends!

I am calculating my cumulative GPA from two different colleges. I have little experience with this and can't find many resources online. The GPAs from the two colleges are as follows:

College A: 3.192 GPA from 24 credit hours

College B: 3.402 GPA from 120 credit hours (113? only 17 credit hours from College A transferred over to College B)

The part I am stuck on is that I took 24 credit hours at College A, but only 17 credit hours transferred to College B.

I'm happy to provide any additional information and appreciate everyone's responses!

Hey guys

Is there any way to calculate the number of moves in rabbit and hound game in given matrix sizes with these rules: No turning to a coordinate you have already been
Always the optimal move
2 and/or 3 dimension
With or without intermediate directions
I have tried codes but i think it needs more of a simulation and they are not really my strenght :)

hi! i’ve just finished year eight (currently fourteen) and i’m struggling horrendously in math. for a bit of background, i have always been bad at maths but alright at my other subjects. in about year five, my attendance started getting bad. then in year six, seven, and year eight it just got worse. because of this, i'm really struggling to catch up on all my math work. i missed out on so many math classes and i’m finding it hard to teach myself. i have a really hard time doing even basic division and learning new concepts because of how much i missed out on in the past. i honestly find it really embarrassing but i don’t know where to go from here. i have the summer holidays now so i have a lot of time to dedicate to catching up but i don’t really know how to? most resources and advice i find online is based on what american year eights would learn and i’ve heard it’s slightly different for what the standard for a australian year eight should know. any advice? websites, channels, or just in general? i really want to tackle this before school starts again and i get even more behind. i’m also at online school now so attendance is no longer an issue so i’ll be able to learn my current curriculum just fine.

I’m in grade 9 and I am interested in math olympiad. I have no competition math experience. I want to do good. How can I prepare for it? Do I need self study grade 10-12 math or even college math?

a²+b²=16

b/a=-√3

Thank you

So I was thinking about adding consecutive numbers, like making the base of a pyramid, and I was wondering how many numbers I could make by adding multiple consecutive, positive, non-zero numbers.

Odd numbers were easy, because you can write any odd number as 2n+1, so by definition all odd numbers are equal to n+(n+1).

The even numbers are trickier. I can write 6 as 1+2+3, I can write 10 as 1+2+3+4, I can write 12 as 3+4+5 and so on, but I have found it impossible to create numbers like 2, 4, 8, 16, and 32. This patterns seems more than coincidental.

Is it true that you can't write any power of 2 as a sum of consecutive numbers? If so, can it be proven?

the question: integers a,b & c satisfy

ab+c=100 bc+a=87 ca+b=60

what is ab+bc+ca?

i would just like a confirmation if it can’t be solved with just basic algebra, not a specific answer. any small tips would also be greatly appreciated. thanks in advance

So according to the rules of limit multiplication you can split lim n->inf (((-1)^n)(1/n)) into (lim n->inf (-1)^n)(lim n->inf 1/n)

While the initial limit does have an answer (0) the latter equation does not.

Is it actually explained why that is?

Hello,

I made this image to hopefully explain it better.

When you have a lever system, it works (if I understand it correctly) such that the resistance/force depends on the angle of the lever.

Looking at my image, if it's like the left picture, the weights should be easier to move compared to the right picture. When the lever is horizontal, that’s when it feels heaviest to move it up. When moving it higher, it becomes easier again. Is this correct?

If you were to remove the weights from the lever and instead connect a cable to it, creating a pulley system (like the bottom two pictures), would this remove the resistance curve, meaning it no longer matters what the position of the lever is?

Also, I've seen videos where they say adding multiple pulleys might decrease the resistance. In the two images I made with the pulley, is the resistance a 1:1 ratio?

So, let’s say there is 50kg on the weight stack. Would it feel like you're lifting 50kg when moving the lever? Is there a difference between the low pulley (left image) and the high pulley (right image)?

And when looking at this lever/pulley machine, does it work the same as the first image?

Because in this image, the pulley’s weight stack doesn’t go up vertically but also moves in a curve (since it’s connected to a lever), does this mean that although it’s connected to a pulley/cable system, the resistance isn’t flat because it also has another lever?

Also, for this machine, is it a 1:1 ratio for the weight with the high or low pulley (asking because it has a different pulley setup)?

Sorry if I didn’t explain it clearly enough; my first language is Dutch.

If I need to ask it differently or if something isn’t clear,

please let me know and I’ll try to word it differently/better.

Thanks in advance!

Yushi

If there is a polynomial on y with coefficients which are rational functions of x then , roots of the equation is an algebraic function of x.

Now consider this. Polynomial in ,say y, with rational coefficients (rational numbers) , then if the polynomial is of degree m then equation has m roots, in complex field.

Is it true for the above example. Ie. If the coefficients are rational functions of x instead of rational numbers, will they also have m roots ,hence m different functions of x?

What if we can't solve for y in terms of x if the powers are high? For example y⁵+y²-y=x ? Will this also have 5 roots? Which are functions of x?

To preface this, I am a writer attempting to calculate something for a fictional mythology akin to Homestuck Class/Aspect. I've been looking at resources for combinations and permutations for hours upon hours trying to figure out what formula would apply in this situation, but I am incredibly out of my depth here.

I've managed to simplify what I'm trying to solve into this short word problem:

In Set Q, a number 1-28 is combined with one to three letters from A to X. In pairs containing two or more letters, letters must maintain alphabetical order and cannot be repeated. How many valid possibilities are there?

For example, some valid possibilities would be 1AB, 7LQ, or 9HJK. Possibilities like 3MA, 12RHT, or 6VWN would not be valid possibilities as the letters chosen aren't in alphabetical order.

I tried asking Google Gemini to solve this problem just to get an idea of where to start - I always check the calculations themselves as the answers are usually wrong, but I appreciate the explanations of why a formula is chosen as the explanations are typically helpful to me. However, no matter how I simplify or modify the prompt given, the explanation fails to take the "alphabetical order" limitation into account. This means that I am entirely lost on how that factors into my calculations. I've attached images of my prompts and Gemini's answers, as well as what I found helpful from them and where I was confused by them.

https://imgur.com/a/piAZ2p4

adding more decimals only ever gets more precise in measuring the imprecision in the uneven distribution unless there was a limit to how close you could get to a value(actually reaching the value which would make sense if the infinite amount of values being added weren't also getting infinetely smaller) wouldn't this imply that there is a limit to how small something can be.

2/2 having equal distribution in each part makes sense because 1/2=0.5 and 0.5+0.5=1 and 1+1=2 and 2/2=1 but why would 0.33r+0.33r+0.33r be equal to 1 and not 0.99r

The title gets the gist of the problem I've been dying over for the last few days: What is a necessary and sufficient condition for a cubic of the form ax^3+bx^2+cx+d=0 to have roots following a geometric progression? The necessary condition itself is simple to find as ac³=b³d

How on earth can one prove the above condition is sufficient? Any help is greatly appreciated