I emailed the author. She said that the meaning of these two symbols were placed only under the first Exercise Set of each Chapter, rather than in the Preface. "Appendix B contains either full or partial solutions to all exercises with blue numbers. When the solution is not complete, the...
Maybe it's explained somewhere in her book, but what do the Hs and *s mean beside some of the problems in Epp's Discrete Math, 4E textbook?
Are there any other notations I should make note of in the book as well?
Thank-you for your help.
What would be the point of knowing information about the subtangent and subnormal lines? Do they have any worthwhile real-world applications? Wikipedia says that they are archaic and fell into disuse after the early 20th century.
Thank-you
I was wondering if anyone could please check my work and reasoning for this problem. Thank-you! (Also, would this be considered a direct proof? How might a contradiction and IFF proof look like and compare?)
Problem: Suppose F, G1 and G2 are nonempty families of sets. Prove that if F ⊆ G1 ∩ G2...
Suppose a certain function in continuous at c and (c. f(c)) exists, then which of the two could be false: \displaystyle \lim_{x \rightarrow c^-} {f(x)} = \lim_{x \rightarrow c^+} {f(x)}, and \displaystyle f'(c)?
I feel like both could be false, because if the formal derivative at a point...
If someone can check this, it would be appreciated. (Maybe it can submitted for a POTW afterwards.) Thank-you.
PROBLEM
Prove that if $H$ and $K$ are torsion-free groups of finite rank $m$ and $n$ respectively, then $G = H \oplus K$ is of rank $m + n$.
SOLUTION
Let $h_1, ..., h_m$ and $k_1...
Hi shamieh,
I'm not quite sure what your post is asking, but as greg1313 pointed out $\pi$ is defined as the circumference of a circle divided by the diameter of the circle. If you were to measure these lengths with increasing accuracy, then you would get closer and closer to the value of $\pi$...
I'm trying to make a check list of courses I need to study and review for the GRE Physics Subject Test. I have a few questions following the list. Thank-you for any help.
Engineering Physics I
Engineering Physics II
Modern Physics
Electricity & Magnetism
Statistical Mechanics & Thermodynamics...
Homework Statement
Find an equation of the tangent lines [in point-slope form] to the hyperbola x^2 + y^2 = 16 that pass through the point (2, -2).
Homework Equations
Point-slope form: y - y_1 = m(x - x_1)
Slope: m = \frac {y_1 - y_0} {x_1 - x_0}
The Attempt at a Solution
First, take the...
Homework Statement
In a plane, find the resultant of a 300-N force at 30^o and a -250-N force at 90^o. Also, find the angle \alpha between the resultant and the y axis.
Homework Equations
x = F cos \theta
y = F sin \theta
r^2 = x^2 + y^2
\theta = tan^{-1} (\frac {y} {x})
The Attempt at a...
I just want to say that if you just stick with tutoring these classes to students at your school, then you'll probably be fine.
...But once you start tutoring it to a wider range of students at different schools, then you'll have to develop a deeper understanding of the material. Because you'll...
\frac {dy}{dt} = y^3 + t^2, y(0) = 0
My teacher said this IVP couldn't be expressed in terms of functions we commonly know. I was wondering what the general solution is?
Thank-you