# Tag Info

## New answers tagged education

4

This forum is about mathematics, and while career advice is sometimes found on here, your particular situation really requires career advice external to the mathematical sciences. ("What are your goals in life? What do you really want to do?" Etc.) I suggest you ask on academia.SE, but even those folks may not be the right crowd. You are looking for very ...

0

I am also software engineer and wish to study maths as extra subject to gain knowledge (not for research for now). Can anyone suggest me any online and distance learning course available in maths .

0

Lots of people use discrete mathematics as a first proof-based class. However, it's not strictly required for linear algebra. A good chunk of linear algebra is computational, and not really focused on theorems and proofs but on solving problems. You could really just dive in and see how much of it makes sense. You might find that a lot of it does. Other ...

0

I would recommend Gelfand, Shen - Algebra but its price is ~22 dollars. Furthermore, you can find a lot of video courses on algebra here which are free and have the advantage of being beginner friendly. I hope this helps. Best wishes, $\mathcal H$akim.

2

Set theory is absolutely necessary to learn more advanced mathematics. It is needed for just about every branch of mathematics, if not every branch. In my opinion, it would be a good idea to start learning some basic set theory notions at least. It will definitely show up in classes like real analysis, complex analysis, and probability just to name a few. ...

1

Learning math is difficult; it takes work. Euclid stated this quite nicely: "There is no royal road to geometry." What should teachers do? Encourage, prod, and guide students into doing that work. Obviously, requiring too much or too little isn't good. Any decent teacher will try to find a good balance. Of course, a teacher can pointlessly 'make things ...

3

Pick your favorite expression that is zero but not easily simplified to zero by the CAS. Then divide by this zero and deduce all kinds of absurdities. Another place a CAS go wrong is properly dealing with branch cuts, and keeping track of domains of validity for various expressions. These and other problems have been discussed in the literature. A good ...

0

just google for algebra, lecture notes, filetype:pdf or something like that http://www.maths.usyd.edu.au/u/bobh/UoS/rfwhole.pdf

2

Most university-level math education has conformed to a left-to-right standard, regardless of how the native language is written. However, pre-university education differs, and it depends on the region. For instance, see here: http://en.wikipedia.org/wiki/Modern_Arabic_mathematical_notation. One of the reasons for the predominance of left-to-right ...

-1

Just put in some parentheses, and then you don't have to worry about the LTR-vs-RTL issue. The expression $(a-b)-c$ means the same thing everywhere.

0

Answer: I have worked out the answers for the most part but try to work through the problem yourself and verify answer with this. Good Luck.

0

I first discovered that math was beautiful upon learning the divisibility rules. At that point I was just like "IT WORKS IT WORKS! HOW DID PEOPLE KNOW THAT?!" I remember I once stayed up to test the divisibility rule of dividing by $8$ (if the last three numbers in the dividend are divisible by $8$ then the whole number is divisible by $8$).

1

Let $\mathbf{P} = (3,1)$ and $\mathbf{Q} = (-4,-4)$. Then a vector equation for the line is $$\mathbf{X}(t) = (1-t)\mathbf{P} + t \mathbf{Q}$$ You can easily check that $\mathbf{X}(0) = \mathbf{P}$ and $\mathbf{X}(1) = \mathbf{Q}$. Alternatively, you could define a vector $\mathbf{V} = \mathbf{Q} - \mathbf{P} = (-7,-5)$, and then the vector equation could ...

0

To find parametric equations x(t) and y(t) you need a vector and a point. Notice you already have 2 points that you can use. Do you know remember how to find a vector? v = < x_2-x_1,y_2-y_1 > Then use the form x(t) = x_1 + tv_x and y(t) = y_1 + tv_y

2

It seems to me you're on the right track to succeed in your life goals, though as I'm sure you know, take your own ideas of how things 'ought' to turn out with a grain of salt -- life is full of surprises. The first point I want to address is that of programming being 'bland.' Math can be bland too. In fact, any time you get to a research level, you will be ...

2

If you can be good at it, majoring in math always majorizes other options - grad and professional schools (e.g. law, medical, etc.) always love a math major. With a math major you can later specialize to anything you want with a masters or professional degree, e.g. computer science. So it's an easy choice assuming you think you can get A's...

9

There's a mistake in your first attempt: $$x = \frac{10!}{8!} + \frac{10!}{9!} = 10 \times 9 + 10 = 100$$

0

Since you are asked about the relative profit, the volume can be set arbitrarily. Take the amount for both acquisitions to be 8. So he is out 16 rupee and has 8*11+8*10 sweets to sell, or 21 repackaged packets. Now you should be able to come to the conclusion...

-1

I must have been very small, around three of four, when I suddenly dashed out of my room, full of excitement, wanting to show my dad something that had made a great impression on me. I held a book, it's front cover facing me. In a flash, I gave it two half-turns. One upside-down, the other left to right. This is what came out: I held my breath, as the ...

0

Since “canceling” means “dividing the numerator and the denominator by the same (non-zero) number” one might cancel the given fraction by $7$, e.g., which yields to $\dfrac{\dfrac{3x^2}{7}-\dfrac{1}{7}}{\dfrac{x^2}{7}},$ which is perfectly right and perfectly senseless either. Moral: canceling means not simplifying per se. If simplifying is the goal, ...

0

Anything trig over/above something not trig. 1.a. unlike trig functions. Anytime there exists a higher power of a variable above or below some smaller power. Anytime there is a constant above or below with addition or subtraction operators with variables. And of course this is all given that a series of variables with powers doesn't equal the below or ...

0

I suggest you have a look at the courses on coursera. In particular the machine learning course, which is arguably the original and best course on coursera, is just about to run. This should give you a good intro to the maths that's relevant for data science in the context of the techniques that are used to do the analysis part of it. In my opinion the ...

0

I recommend getting several Schaum's Outline Series books that are related to the subjects you want to work on, such as the following: Probability, Random Variables, and Random Processes Theory and Problems of Real Variables; Lebesgue Measure and Integration With Applications to Fourier Series Advanced Mathematics for Engineers and Scientists

0

Above all else, keep working hard and stay positive. Believe that you are capable, because chances are, you are. I am pursuing a Statistics Grad degree and my undergraduate is in Sociology. One thing that I found that has helped me is using a ti-89 calculator. I know some will shun me for suggesting this, but it is a helpful tool. The reality is that you are ...

-1

This is more of English language issue than math issue. Let $v$ denote the original value. To say that something "increased by x% of original value" means the new value is $v+\dfrac{x}{100}v$. To say that something "spiked to x% of original value" means the new value is $\dfrac{x}{100}v$. I emphasized the prepositions, because they are what makes the ...

2

I explain the "horizontal shift" this way: when we graph $\ y = f(x+h) \ ,$ we are composing $\ f(x) \$ on the function $\ x + h \ .$ This is to say that we are first adding $\ h \$ to $\ x \ ,$ evaluating the function $\ f \$ at $\ x + h \ ,$ and then plotting the result at $\ x \ .$ This has the effect of reading off values of the ...

0

Your claim is that for any (reasonable) difference between $t_1$ and $t_2$, we have that $\frac12(r_1+r_2)$ is a constant. I argue that the claim you're making is quite strong. Even if it were true [and it turns out it isn't], most of the solution would probably be wrapped up in it. For example, the claim is not true for a fixed distance: from $d=rt$ we ...

0

They don't meet in the middle, but further away from the starting point of the faster one. And one thing that is often the cause of erorr in such problems is to take the wrong kind of average of velocities: Sometimes arithmetic mean is correct, sometimes harmonic mean, sometimes we better make a sketch. In fact, a sketch (location-time-diagram) is the best ...

2

One way to detect that an exercise has some importance is if its result is used later in the text. As for lists of crucial but omitted results... well, I doubt such lists exist, and if they did, they'd omit things too, and people would object to those omissions. Not because every subject has a canonical list of crucial results and authors neglect to ...

1

I'm not sure there is an efficient way of finding out. The best way I know of is to consult a variety of textbooks. Different authors have different ideas of what is important.

1

Check out the little result this gentleman implies with his logic in his video... Let S be the sum in question, ie: S:= 1+ 2+3+4+.... Now S can be rewritten in three ways.. here's the first: S= 1+ 2+ 3+ 4+.. (By the uniqueness of additive inverses and the closure of Z under addition:) =(2-1)+(1+4-3)+(3+6-6)+(6+8-10)+.... (by associativity we have) ...

2

If I understand correctly, are are asking about the following. You can think of any normal subgroup as a kernel of some homomorphism, and vice versa. It is obvious that any kernel is a normal subgroup. From the other hand, if $N<G$ is a normal subgroup, then it is the kernel of the canonical homomorphism $G\to G/N$ sendeing $g\mapsto gN$. It is ...

2

Your question suggests she understands not just multiplication but exponents. If that's not the case, you might want to start with the former. (The latter you can think of as a special case of the former.) In that light, one way to teach multiplication — though I imagine the multiplication table should come at least as early as this — that I think ...

1

If $a=1$, then there's nothing to prove. The square with side length $1$ just happens to be what we choose to measure areas in. For an integral $a>1$, you can divide the large square into unit squares, and if the child understands multiplication at all (otherwise all is lost), it should be clear that the area of the large square is $a\cdot a$. If $a$ is ...

5

Area might better be introduced with rectangles and $a \times b$ before you move on to squares, especially if you start with $2 \times b$. I would suggest wooden cubes: the ones with letters of the alphabet are probably ideal.

1

i just spent an hour agonizing over that too....eventually found that question is missing some info. This guide has the correctly worded question... www.aes.gov.nl.ca/app/exams/pdf/StudyGuide_RefrigAirCondMech.pdf‎ there are 2 defrost heaters not listed which add another 12 amps.

0

Your answer is correct given the data we have. The motors will presumably have a higher starting current than running current, so in real life you need to allow for that. 20A is substantially higher than needed, however.

1

Let $y=\sqrt{x^2+1}$. Then, squaring gives $y^2=x^2+1$, and thus $\sqrt{x^2+1}$ is the root of the following polynomial equation: $$y^2-x^2=1$$ It is therefore an algebraic function.

1

Get Friedberg, Insel and Spence's "Linear Algebra" 4th edition, sit down, and do every non-computational problem in the first three chapters. It's my favorite math book. It introduces linear algebra via an axiomatic approach that you'll probably see often as you go on in math. It's rigorous, it provides intuition and a meaningful framework to linear ...

2

The tension between following abstract rules as against intuition has been present in mathematics for centuries if not much longer. From the time of Newton and Leibniz onwards mathematics became more algebraic due to the calculus. For example, the eighteenth century mathematician Lagrange played a critical role in moving away away from diagrams towards ...

4

No, don't abandon your love of analogies and your search for connections to the "real world". But a caveat: be guided by it, not shackled to it. A few more remarks. (1) Linear algebra can be presented sevaral different ways: computationally, conceptually, geometrically, physically, etc. It sounds like you've encountered a mismatch between your course and ...

1

Linear algebra (and also functional analysis to some extend) are fields where it's still possible to have geometric interpretations. Linear transformations (in particular, matrices) can represent reflections, rotations and scalings which transform vectors. You lose some exact graphical interpretation when you move from 2- and 3-dimensional vector spaces to ...

2

Linear algebra is by no means about computations over concepts. There's actually a rather precise dichotomy that approximates that between computations and concepts in linear algebra, namely that between matrix algebra and the theory of abstract linear transformations. It's from the latter perspective linear algebra most naturally displays its ability to ...

2

You've written this post as a leading question, you'll get much too bloomy answers. My advice is to search for the motivations behind the introduction of this and that concept - knowing that these exist will let you concentrate on the plug and chuck you need to get your answers. I want to add that not all mathematical object are physical things - e.g. the ...

0

Whittaker and Watson. Hardy, Wright, and Hardy and Wright learned complex analysis from it.

0

Complex variables: An introduction, by Carlos A. Berenstein and Roger Gay (Springer, 1991). An underrated masterpiece. This is a self-contained, very accessible, comprehensive, and masterfully written textbook that I do find very suitable for the serious self-taught possessing the rare mathematical maturity, and being in command of a quite modest (but not ...

0

Instead of entering a discussion about the proof for real numbers, I would propose discussing instead the abstract version, which gives far less opportunity for polemic. Let the "crank" decide what he thinks about the abstract version and its proof, and then see where to go from there. If he refuses the abstract version, he should either be able to find ...

0

I have the same problem. Until now, old books have been my best sources of interesting problems. The most interesting applications to diff. eq. I have found are: Time of death of a corpse (a heat transfer problem in disguise). Found in Boyce & Diprima, 4th edition, this problem is interesting, but your students need to master solving the equation y' ...

1

Although math is a very strict formalistic language, sometimes knowing rules and formulas just isn't enough to understand what's happening. Mathematics is not just about being able to understand the mathematical language. It's about understanding concepts and structures. Personally, I use a lot of imagination, especially in Real and Functional Analysis and ...

10

It depends on the person. Sometimes they use their own script which is not yet ready to publish. Sometimes there is no good book for all lectures, but for all lectures there is a good book (that is, different for each). Sometimes the book the examples/questions come from is good only for those who already understand the topic (i.e. it is bad for ...

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