Mathematics

One solution to global warming could be to view greenhouse gas emitting objects as an ecosystem. In that ecosystem would be vehichles, factories, etc. Once the ecosystem of greenhouse gas waste is identified, it would be possible to deduce how that ecosystem mates wth the human race. Vehicichles, a mathematical function of the human need to travel efficiently. Factories, the result of human desire to produce goods and services quick time. Efficiency, therefore is the key propellant of greenhouse gases. There is the need for efficiency over a broad range of human activities, therefore, there is greenhouse gases. True or false? So how to …

Hello people! I've started studying math on my own. I'm currently in high school, and there we are currently at quadratic equtions. I want to know what order of self-studying mathematics do you recommend? I started trigonometry course for beginners on youtube, and I want to cover them all one by one, trigonometry, logarithms, and sometimes in the future differential equations and calculus. I'm curious what do you think is the best order to do it? Mainly I'm interested in math because I want to pursue a career in physics or/and astronomy so I want to learn as much as possible so I don't have to do it later in life. Also, besides the order of studying, are there any co…

Let us consider a transformation $T$, which converts a vector into a symmetric matrix, e.g. Xh=[x1,x2,x3]T , then \(T(X_h) =. I want to have this type of decomposition: T(QXh)=Q¯T(Xh)Q¯T. Here, $Q\in \mathbb{R}^{m\times \frac{q(q+1)}{2}}$, $\bar{Q}\in \mathbb{R}^{p \times q}$, $T(X_h)\in \mathbb{R}^{q \times q}$ and $X_h \in \mathbb{R}^{q(q+1)/2}$. For example: Consider a known constant matrix $Q \in \mathrm{R}^{10 \times 3}$. A vector $X_h = [x_{11}, x_{12}, x_{22}]^T \in \mathrm{R}^3$. Decomposition must be like, T(QXh)=Q¯T(Xh)Q¯T=Q¯[x11x12x12x22]Q¯T where, $T(QX_h)\in \mathrm{R}^{4 \times 4}$, $\bar{Q…

I grok, am NOT asking about, the answers below. Rather, how can I calculate the final answer DIRECTLY, without division? I don't know why my Latex isn't rendering here? Please see https://math.codidact.com/posts/285679. Orange underline 1. Unquestionably, $\color{#FFA500}{4 \times 3/2} = 3!$ But how can I construe 3! DIRECTLY WITHOUT DIVISION? What does 3! mean? Here's my surmisal. Blitzstein's solution hints to this calculation, but he didn't write 3! explicitly. You fix the first person. Then of the 3 people left, you can pick the 2nd person in your 2-person committee in 3 ways. Is this correct? Red underline 2. Unquestionably, ${\color{red}{\d…

My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof?

The Collatz conjecture concerns sequences defined as follows: start with any positive integer n. Then each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no matter what value of n, the sequence will always reach 1. Here's a directed graph showing the orbits of small numbers under the Collatz map, skipping even numbers. Anyway, mathematicians keep saying this is beyond the reach of present day mathematics. Wonder if humans will solve this about the time we get n…

I have been asked by a member to comment on this worked example question encountered in an online tigonometry course. The temperature during the week oscillates daily between 48o and 74o. (presumabably Farenheit). If the minimum occurs at 5am, at what time is the temperature at 65oF ? The lecturer chooses a sinusoidal model for the variation, but uses a very overcomplicated method where he arrives at and solves the following equation. [math]f\left( \theta \right) = - 13\cos \left( {\frac{\pi }{2}\left( {\theta - 5} \right)} \right) + 61[/math] Here are my comments. The lecturer has chosen to use a cosine wave as the model, using rad…

I want this thread to be an attempt to create a generalized overall mapping of mathematics as we know it at this current time. Its basis is that all models developed by a human is itself a model, therefore I do not want to delve to deeply into the philosophy of the subject matter, whereas I would like for this to be an overall model of existing mathematics from beginner to expert levels all explained and viewed as a general "mapping." Showing the interconnections between all of the different mathematical concepts formed which have been agreed upon. Showing all the twists and turns, all the connections, all of the branches that lead to no where. This is a big pr…

A quick "google" with give you several definitions of mathematics. To me they tend to be necessary, but far from sufficent. As example; Mathematics is the abstract study of numbers, shape, structure and change. Numbers are part of mathematics, so are simple geometric shape, by structures we mean patterens and relations between them, and differential calculus ("rates of change") are all parts of mathematics. This definition seems okay, but a little vague and it may not be very clear what we mean by a structure. Also, as mathematics evolves, solutions to problems often come from outside the area the problem was initially defined, any defintion must be able…

Hello! 1st post... really nervous, because I am "et up" with academic elitism and don't want hero's worshipped remotely bursting my adoration with harsh retort to my naivete. Consider I'm six years old. (Actually 67, retired from software development, but work with me.) I found an anomaly in general summation, Fibonacci style -> F(n) = F(n-1) + F(n- 2) Algebra and computer science was fun, and the fun went to amazement when two seed numbers for general Fibonacci summation produced adjacent sequence numbers with a divisor that is not (it is not) an approximation of the golden ratio. The quotient of adjacent sequence numbers is -1/Phi = -0.61803... [Big, bol…

Prove whether the below statment is true or false. Statement - 1) Calculate 72 × 1 + 36, 72 × 2 + 36 ......72 × n +36. 2) Add all the sums e.g 108 + 180......+ 35 = n (along with 35 once to get total sum as 'n'). 3) The total 'n' must be p×q= n. Where p and q can be, Twin prime × Twin prime. Prime number × Composite number ( not divisible by 2 or 3, having a gap of 2). Composite number × Composite number ( not divisible by 2 or 3, having a gap of 2 ). This theorm shows how one can instantly factor larger, largest product 'n' …

Hi all, Why say that the following phrase is nonsense? “The consistency of axioms cannot be proved within their own system.” Because: A system which has axioms for itself, in order for the system to call them axioms for itself, the system has to have a consistent behavior around those axioms and so when it behaves inconsistently with regard to those axioms, the inconsistency between those axioms and the system’s behavior the system can prove to itself. If what is written above is false, then when a system behaves inconsistently with regard to some axioms it has for itself, that inconsistency it cannot prove to itself, and it keeps behaving inconsis…

Why are numbers between 0 and 1 fractions? And what base uses this "rule"? Base 10??? As in % ??? Hopefully this question doesn't receive "scrutiny" It's ok if nobody doesn't know the answer..lol

I saw this question at https://math.codidact.com/posts/283253.

If a/b is greater than 1 than b/a must greater than 0 but less than 1.<br><br> For every number greater than 1 there is a multiplicative inverse greater than 0 but less than 1. <br><br> Examples 3/4-4/3, 7/8-8/7, 9/10-10/9, 1/3-3/1, 3/5-5/3 <br><br> But is there a proof for this?<br><br>

Pie value continuation

I couldn't help but wonder if anyone knows how raising e to the imaginary pi power could result in a negative number. In this case, -1. https://en.wikipedia.org/wiki/Euler's_identity Different values of pi can result in different numbers, like 2pi would give a positive one. Then it seems that raising e by a multiple of imaginary pi powers can result in a positive or negative answer. For example, you wouldn't ever be able to raise 1 to an imaginary pi power to ever get a negative answer. You would always just get a positive one. How is e so much more special than 1 to where it's imaginary pi powers can be negative. Then you can raise 2 to an imaginary power…

So one of my pet peeves back when I was into image editing is that in trying to stack images of different aspect ratios vertically such that they'd have the same width; or juxtapose them horizontally such that they'd have the same height; it was always a long, drawn-out game of guess and check to get it right, or at least close enough to right that I could crop it from there. (For the record, I'm referring to Cracked.com, where the combined width in question had to be equal to or fewer than 550 pixels, and the combined height equal to or fewer than 750, rather than outright shrinking one down to and only down to the width or height of the other. Cracked.com is no longer d…

This shows something that appears to be a contradiction in ZF: https://arweave.net/RJ4DRuRjdVWqJ5RBHB30SXDBXATzqmAV3Qs1b6f1ykw (Note that by set-definition I mean it's numeric code, in an encoding such as Godel's encoding.) What the heck? What's wrong? --- It seems I understood why the error: S is a function in a model of ZF, not in the formal system the proof is written. So, it's illegal to use it in the proof. That's a very beautiful sophism. What happens if we try to define S inside ZF? It should fail (unless ZF is contradictory). But how does it fails? That is an practically useful question, because I …

Not even sure how to begin with something " imaginary" and build insight through questions on this, " seriously." From my book on Elementary And Intermediate Algebra, page 584. Talks about the ideas behind the use of a number that is a square root of -1 also referred to as i Uhmmm, Ok.....So then " where did complex numbers come from then?? The page goes onto to mention how negative numbers do not have negative squared roots... Understood, however then it says: Larger number systems that contain the " real number systems" " Real number - Wikipedia" is designed so that negative numbers do have squared roots. Ok....…

I could use recommendations for self study intended to revise a maths unit where I did poorly. General topic is Introductory Calculus and Linear Algebra. The rest of this post is simply detail as to where I am and where I hope to go - so skip if bored. I completed precalculus with flying colours but fell apart in MTHS120 Calculus and Linear Algebra 1. I think I am actually fine (with a little revision) on the basics of integration, differentiation and matrix algebra. Worryingly my issue seems to have been at a deeper conceptual level. I am not permitted to repeat a unit that I actually passed but I have pretty much a whole trimester with no formal study later this ye…

Cracked it in 5 seconds. If you don't know what Kryptos is, read this. CIA website This is so funny. There's no coded messages there!!! Kryptos

For example I asked around the proof of for 1 + 1 = 2 or mathematical proof for any addition and people mentioned different mathematicians for the proof. What is like the standard that is used as the foundation of mathematics. I took high school math but that is about it, I know from a little reading that there are axioms which I think are the foundation of math. Is there a place where these axioms are collected into one?

Good Basic mathematics or Pre-algebra books were hard to find Then i found some good materials here , Pre-Algebra https://www.math-only-math.com/ Algebra https://nios.ac.in/online-course-material/secondary-courses/Mathematics-(211)-Syllabus.aspx I am planning to spent at least 1 hour daily to learn Basic mathematics and Algebra I am trying to prepare for a test , that is why i wanted to learn all these from the beginning Now i need to find me some energy and motivation to sit and practice these books daily for at least 1 hour I am planning to study after 11 at night everyday , since i have to work till evening 6:30 everyday …

(61/2 - 21/2)/4 = (2 - 31/2)1/2/2 I have taken sin * cos=1/4 then I have got sine=(2 - 31/2)1/2/2 or (2 + 31/2)1/2/2 Calculator has shown arcsin=15 degrees but sine 15 degrees=(61/2 - 21/2)/4 I don't understand how they are connected.