Beat Unknown Soldier at his own game of math.

[steve_bank]

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n²+ n.

Seriously your mathematical problem statement is incomprehensible.

Here is one,

You have $10.00 total.
You have 3 $1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form.

Ill-formed. 3+1.25+.40+.20 ≠ 10

Here's one for you.

Find the generating function that counts how many ways $10 can be made up from dollar bills, quarters, nickels, and dimes.

I can't off the top of my head.

Now if want to numerically or via LaPlace Transforms solve linear homogeneous differential equations that would be a different matter.

Artificial useless problems never interested me.

 

[Juvenal]

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n²+ n.

Seriously your mathematical problem statement is incomprehensible.

Here is one,

You have $10.00 total.
You have 3 $1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form.

Ill-formed. 3+1.25+.40+.20 ≠ 10

Here's one for you.

Find the generating function that counts how many ways $10 can be made up from dollar bills, quarters, nickels, and dimes.

I can't off the top of my head.

[x^1000] (1/1-x^100) * (1/1-x^25) * (1/1-x^5) * (1/ 1-x^10)

Now if want to numerically or via LaPlace Transforms solve linear homogeneous differential equations that would be a different matter.

I am a professor of pure mathematics. Save your double-talk for someone else. I've taught LaPlace transforms and differential equations. You don't use the former to solve the latter.

Artificial useless problems never interested me.

vs.

Here is one,

You have $10.00 total.
You have 3 $1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form.

Your petard, it has hoisted you.

 

[Swammerdami]

Here's one for you.

Find the generating function that counts how many ways $10 can be made up from dollar bills, quarters, nickels, and dimes.

It's delightful to finally see an actual mathematician show up in the thread!

 

[steve_bank]

1.
x + 2y = 10
2x + 3y = 18
x + 2y -10 = 0
2x + 3y – 18 = 0
x + 2y – 10 = 2x + 3y -18.
-x – y + 8 = 0
x + y = 8
y = 8 -x
substituting in the first equation
x + 2(8 -x) = 10
x + 16 – 2x = 10
x = 6
y = 8 – 6
y = 2

2. Subtracting two lines
2x + 3y = 18
x + 2y = 10 -
---------------
x + y = 8
y = 8 – x

3. Matrices

x1 + 2*x2 = 10
2*x1 + 3*x2 = 18

A =
1 2
2 3
b =
10
18
A*x = b
x = b/A
x = b*A’ where A’ s the inverse of A
x =
2
6

Math tools operate directly on matrces making it easy.
Linear in linear algebra refers to lines.


x + 2y = 10
y = (10 – x)/2
y = -.5x + 5

Which is the form of y = mx + b where m is the slope and b is an offset.

2x + 3y = 18
y = (18 – 2x)/3
y = - x*2/3 + 6

The meaning of the simultaneous solution is the intersection of lines in space or on a graph.

I thought I made the seond problem non linear which means it can not be solved using linear algebra. It erequires a non linear solver.

Non linear equations can not be solved byAx = b.

There is beaucoup videos and sites on this. Common knowledge and application .

A good placeto start tp understand linear algebra.

https://www.mathcentre.ac.uk/resources/uploaded/sigma-matrices8-2009-1.pdf

 

[steve_bank]

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n²+ n.

Seriously your mathematical problem statement is incomprehensible.

Here is one,

You have $10.00 total.
You have 3 $1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form.

Ill-formed. 3+1.25+.40+.20 ≠ 10

Here's one for you.

Find the generating function that counts how many ways $10 can be made up from dollar bills, quarters, nickels, and dimes.

I can't off the top of my head.

[x^1000] (1/1-x^100) * (1/1-x^25) * (1/1-x^5) * (1/ 1-x^10)

Now if want to numerically or via LaPlace Transforms solve linear homogeneous differential equations that would be a different matter.

I am a professor of pure mathematics. Save your double-talk for someone else. I've taught LaPlace transforms and differential equations. You don't use the former to solve the latter.

Artificial useless problems never interested me.

vs.

Here is one,

You have $10.00 total.
You have 3 $1 bills.
You have 5 quarters.
You have 8 nickles,
You have 2 dimes.

How would you algebraically find how many pennies and additional nickels would you need you have to equal $$10.00? In equation form.

Your petard, it has hoisted you.

I am awed by your presence.

(x | y) = (1 2 | 2 3 )^-1 (10 | 18) Is there an answer here?

is (1 2 | 2 3 )^-1 supposed to be the inverse?

The ' is typical used to indicate the inverse. A' A prime. Maybe mathematicians do it diferently.

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

As to the con prblem there are a number of combinations of pennies abd nickels. The reult shoud be an equation N and P. I rememberes the problem from high scool algebra.

Again a very simple problem,

 

[steve_bank]

I am a professor of pure mathematics. Save your double-talk for someone else. I've taught LaPlace transforms and differential equations. You don't use the former to solve the latter.

Authority from credentials does not work with me, been around too much.

What on Earth is a professor of math doing on a thread like this? A math prof who coud not resist solving a simple problem?

I applied math in situations for which there were concequnces. The use of and the underlying theory of LaPlace and Fourier Transforms are as common as rain.

Math theory and teaching are important, but nothing special.

The thing is I make no claim to any special matnematcal expertise, never have.

Soldier is the claiming to be a mathematician with expertise in linear algebra.

 

[Juvenal]

A*x = b
x = b/A
x = b*A’ where A’ s the inverse of A

No.

\(x= A^{-1} b\)

Multiplication of a 2x1 matrix on the left with a 2x2 matrix on the right is undefined.

 

[Juvenal]

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

I have first year students who could run circles around you and you want to come after me. You couldn't even understand half of US's questions. This would be a good time to stop embarrassing yourself.

Or not. Everyone loves a good train wreck.

 

[Juvenal]

is (1 2 | 2 3 )^-1 supposed to be the inverse?

I couldn't be arsed to insert the LaTeX previously.

\(\begin{pmatrix} 1 & 2\\ 2 & 3 \end{pmatrix}^{-1}\)

 

[Juvenal]

What on Earth is a professor of math doing on a thread like this?

Busting bullshitters who didn't expect to be called on their bulllshit.

Ask me a hard one next time.

 

[steve_bank]

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

I have first year students who could run circles around you and you want to come after me. You couldn't even understand half of US's questions. This would be a good time to stop embarrassing yourself.

Or not. Everyone loves a good train wreck.

Don't have a clue as to who you are. You jumped into a conversation you were not party to, and loudly solved a simple problem I asked those who know it not to.. That is your trip.

I made a successful career appplying math and science, and building useful things. I am satisfied with my accomplishments, and the peer recognition I enjoyed.

Math is a tool, it is what you can do with it that matters.

I did not ask you a question, I asked soldier. You presumed to answer when I asked those who know it not to.

I am a retired engineer. I spent 30 years paying attention to details in competitive environments where it mattered. Intel and Lockheed in the 80s. If you think you are being competitive in an anonymous forum you really are not.

I make a reasonable effort on the forum, but I do not worry about being wrong. Some act like the form is completion.

You were bored? After 30 years of continuous problem solving I write code to keep boredom at bay. You can look at my preliminary cut at simulating gas molecules in a tank on the programing thread. The kind of modeling I would do on a design problem.

Back in the 80s before widespread PC math tools I wrote my own math library in C. I read numerical methods books and ported FORTRAN to C. There was a book Numeral Recopies In C but it was buggy. That was some 45 years years ago.

I used a slide rule in high school and my first try at college before I went to the Navy.

Something I and peers in y engineering hertion have noticed. New colleg grads seem to be missing something, . An inability to ijdendently attack a problem when tere is no exiting comnter tool or app or solution online avilble. Certainly not all, perhaps a trend.


There is the engennering sterotype of the pendantc engineer always correcting others, but unable to actually get anything done.

I will have a question for you on the math forum tomorrow on La Place Transforms. Perhaps you can answer. I have ben triyng to code the forward and reverse trasforms from scratch as an exercise.

 

[steve_bank]

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

I have first year students who could run circles around you and you want to come after me. You couldn't even understand half of US's questions. This would be a good time to stop embarrassing yourself.

Or not. Everyone loves a good train wreck.

Don't have a clue as to who you are. You jumped into a conversation you were not party to, and loudly solved a simple problem I asked those who know it not to.. That is your trip.

I made a successful career appplying math and science, and building useful things. I am satisfied with my accomplishments, and the peer recognition I enjoyed.

Math is a tool, it is what you can do with it that matters.

I did not ask you a question, I asked soldier. You presumed to answer when I asked those who know it not to.

I am a retired engineer. I spent 30 years paying attention to details in competitive environments where it mattered. Intel and Lockheed in the 80s. If you think you are being competitive in an anonymous forum you really are not.

I make a reasonable effort on the forum, but I do not worry about being wrong. Some act like the form is completion.

You were bored? After 30 years of continuous problem solving I write code to keep boredom at bay. You can look at my preliminary cut at simulating gas molecules in a tank on the programing thread. The kind of modeling I would do on a design problem.

Back in the 80s before widespread PC math tools I wrote my own math library in C. I read numerical methods books and ported FORTRAN to C. There was a book Numeral Recopies In C but it was buggy. That was some 45 years years ago.

I used a slide rule in high school and my first try at college before I went to the Navy.

Something I and peers in y engineering hertion have noticed. New colleg grads seem to be missing something, . An inability to ijdendently attack a problem when tere is no exiting comnter tool or app or solution online avilble. Certainly not all, perhaps a trend.


There is the engennering sterotype of the pendantc engineer always correcting others, but unable to actually get anything done.

I will have a question for you on the math forum tomorrow on La Place Transforms. Perhaps you can answer. I have ben triyng to code the forward and reverse trasforms from scratch as an exercise.

aaa

 

[Juvenal]

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

I have first year students who could run circles around you and you want to come after me. You couldn't even understand half of US's questions. This would be a good time to stop embarrassing yourself.

Or not. Everyone loves a good train wreck.

Don't have a clue as to who you are. You jumped into a conversation you were not party to, and loudly solved a simple problem I asked those who know it not to.. That is your trip.

If that's an apology for throwing crap at the walls, it needs work.

I made a successful career appplying math and science, and building useful things. I am satisfied with my accomplishments, and the peer recognition I enjoyed.

Math is a tool, it is what you can do with it that matters.

I did not ask you a question, I asked soldier. You presumed to answer when I asked those who know it not to.

You asked a question on an open thread started by someone else, in an attempt to bust the o/p ... after proving you couldn't even comprehend the o/p's questions. Everybody who could comprehend his questions knew you were bullshitting right then.

And you knew it when you posted your own question, which you then showed you didn't know how to answer. Or more kindly, that you could kind of recall how to answer, but couldn't be arsed to review well enough to get it right.

\(A^{-1}b \neq bA^{-1}\) because matrix multiplication isn't commutative. It's not even defined for rectangular matrices if they don't have the right shape.

The "linear" in linear algebra refers to the degree of the variables, not the geometry.

\(x+y+z=1\) is not a line, it's a plane in 3-space perpendicular to the line \(t(1,1,1)\).

Nobody successfully navigates high school without knowing the multiplicative inverse of \(x\) is given by \(x^{-1}\), not \(x'\).

I mean, really. This is a train wreck.

I am a retired engineer. I spent 30 years paying attention to details in competitive environments where it mattered. Intel and Lockheed in the 80s. If you think you are being competitive in an anonymous forum you really are not.

It's about correcting errors. You're not even close to the first student I've corrected this week, the principal difference being that my students actually fix their mistakes after they're pointed out rather than bulling on after a correction.

I make a reasonable effort on the forum, but I do not worry about being wrong. Some act like the form is completion.

You were bored? After 30 years of continuous problem solving I write code to keep boredom at bay. You can look at my preliminary cut at simulating gas molecules in a tank on the programing thread. The kind of modeling I would do on a design problem.

Back in the 80s before widespread PC math tools I wrote my own math library in C. I read numerical methods books and ported FORTRAN to C. There was a book Numeral Recopies In C but it was buggy. That was some 45 years years ago.

I used a slide rule in high school and my first try at college before I went to the Navy.

Something I and peers in y engineering hertion have noticed. New colleg grads seem to be missing something, . An inability to ijdendently attack a problem when tere is no exiting comnter tool or app or solution online avilble. Certainly not all, perhaps a trend.

There is the engennering sterotype of the pendantc engineer always correcting others, but unable to actually get anything done.

This is Internet Infidels. I've been away awhile, but back in the day, the joy of this board was in asking random questions and watching people from the top of their field rap back atcha, often enough the same day.

A question I asked on Mitochondrial Eve got a response from one of Rebecca Cann's former grad students before I went to bed that night. Per Ahlberg used to hand out preprints to his most recent research on Devonian transitionals back around when Tiktaalik was first discovered.

And you want to bitch because a math professor showed up to bust your chops after you posted some errant nonsense.

FFS, suck it up.

I will have a question for you on the math forum tomorrow on La Place Transforms. Perhaps you can answer. I have ben triyng to code the forward and reverse trasforms from scratch as an exercise.

If you can find the mistakes I included in my answers to the o/p's questions, I'll consider it.

I use that method as a tool to assess comprehension, because students who've truly mastered material know enough to spot my deliberate errors.

And yes, anyone else reading this thread is welcome to "bust the professor" as well. It's okay, that was always the plan.

 

[Unknown Soldier]

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

One form of the definition is (A-B) U (B-A).

That's just the definition of symmetric difference. So your answer is wrong.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

Assumes incorrectly those are the only colas.

That's not true and even if it was true it is irrelevant. Your answer is wrong.

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

a+b+c=1
4a+2b+c=1
9a+3b+c=3

You need to solve that system of equations for a, b, and c. Until you do so, your answer is wrong.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

Area = G(pi)-G(0) with G(x)=-2 cos 3x / 3
(y-2 sin 3pi/6)/(x-pi/6) = 6cos 3x

That's wrong too!

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

xy-6=4 iff xy=10

Great! This answer is actually correct.

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

a, b both positive or both negative -> x=a/b >0 and x+1/x ≥ 2 -> x^2-2x+1 ≥ 0 -> (x-1)^2≥0, corollary ab<0 then a/b+b/a ≤2

That's wrong.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n²+ n.

if n≠0 mod 2, then n+1=0 mod 2 for all n in Z.

Wrong again.

These are beyond trivial.

You got only one of them right. There's nothing trivial about sloppy math.

Try some real math.

I'd recommend you learn some "real math."

 

[Unknown Soldier]

Here's one for you.

Find the generating function that counts how many ways $10 can be made up from dollar bills, quarters, nickels, and dimes.

It's delightful to finally see an actual mathematician show up in the thread!

An "actual mathematician" who flunked my test.

 

[steve_bank]

You jumped in on a simple problem I posed for soldier, so far I am underwhelmed. At least where I was simultaneous equations are routine and ordinary.

I have first year students who could run circles around you and you want to come after me. You couldn't even understand half of US's questions. This would be a good time to stop embarrassing yourself.

Or not. Everyone loves a good train wreck.

Don't have a clue as to who you are. You jumped into a conversation you were not party to, and loudly solved a simple problem I asked those who know it not to.. That is your trip.

If that's an apology for throwing crap at the walls, it needs work.

I made a successful career appplying math and science, and building useful things. I am satisfied with my accomplishments, and the peer recognition I enjoyed.

Math is a tool, it is what you can do with it that matters.

I did not ask you a question, I asked soldier. You presumed to answer when I asked those who know it not to.

You asked a question on an open thread started by someone else, in an attempt to bust the o/p ... after proving you couldn't even comprehend the o/p's questions. Everybody who could comprehend his questions knew you were bullshitting right then.

And you knew it when you posted your own question, which you then showed you didn't know how to answer. Or more kindly, that you could kind of recall how to answer, but couldn't be arsed to review well enough to get it right.

\(A^{-1}b \neq bA^{-1}\) because matrix multiplication isn't commutative. It's not even defined for rectangular matrices if they don't have the right shape.

The "linear" in linear algebra refers to the degree of the variables, not the geometry.

\(x+y+z=1\) is not a line, it's a plane in 3-space perpendicular to the line \(t(1,1,1)\).

Nobody successfully navigates high school without knowing the multiplicative inverse of \(x\) is given by \(x^{-1}\), not \(x'\).

I mean, really. This is a train wreck.

I am a retired engineer. I spent 30 years paying attention to details in competitive environments where it mattered. Intel and Lockheed in the 80s. If you think you are being competitive in an anonymous forum you really are not.

It's about correcting errors. You're not even close to the first student I've corrected this week, the principal difference being that my students actually fix their mistakes after they're pointed out rather than bulling on after a correction.

I make a reasonable effort on the forum, but I do not worry about being wrong. Some act like the form is completion.

You were bored? After 30 years of continuous problem solving I write code to keep boredom at bay. You can look at my preliminary cut at simulating gas molecules in a tank on the programing thread. The kind of modeling I would do on a design problem.

Back in the 80s before widespread PC math tools I wrote my own math library in C. I read numerical methods books and ported FORTRAN to C. There was a book Numeral Recopies In C but it was buggy. That was some 45 years years ago.

I used a slide rule in high school and my first try at college before I went to the Navy.

Something I and peers in y engineering hertion have noticed. New colleg grads seem to be missing something, . An inability to ijdendently attack a problem when tere is no exiting comnter tool or app or solution online avilble. Certainly not all, perhaps a trend.

There is the engennering sterotype of the pendantc engineer always correcting others, but unable to actually get anything done.

This is Internet Infidels. I've been away awhile, but back in the day, the joy of this board was in asking random questions and watching people from the top of their field rap back atcha, often enough the same day.

A question I asked on Mitochondrial Eve got a response from one of Rebecca Cann's former grad students before I went to bed that night. Per Ahlberg used to hand out preprints to his most recent research on Devonian transitionals back around when Tiktaalik was first discovered.

And you want to bitch because a math professor showed up to bust your chops after you posted some errant nonsense.

FFS, suck it up.

I will have a question for you on the math forum tomorrow on La Place Transforms. Perhaps you can answer. I have ben triyng to code the forward and reverse trasforms from scratch as an exercise.

If you can find the mistakes I included in my answers to the o/p's questions, I'll consider it.

I use that method as a tool to assess comprehension, because students who've truly mastered material know enough to spot my deliberate errors.

And yes, anyone else reading this thread is welcome to "bust the professor" as well. It's okay, that was always the plan.

My last cm,ets to you.

You jumped into a conversation tat goes back to sildier’s thread ‘Why mathematics is neither absolutely nor objectively "right."’

He clams that 2 + 2 does not alwys equal 4 in math, therefore math us not absulute and is open to subjunctive interpretation.

As a math prof you may want to read through that thread.

Soldier says he read books on math and that qialifies him as a mathematician. We reacted to his bogus logic as he tries to come up wth clever problems to amaze us, all the while not understanding fundamentals.

As to busting the professor, why would I want to do that? My skill was synthesizing systems, not math trivia. I was never bored trhroughout my adult life.

 

[Juvenal]

Here's a somewhat challenging math quiz. If any of you self-proclaimed math experts can get the right answers, then you will have proved your previous boasts that you are at least as good as I am at mathematics. Feel free to us computers, calculators, and online resources to get your answers--just don't use another person.

I. Lets set A = {1, 2, 3, 4, 5, 6, 7} and set B = {4, 5, 6, 7, 8, 9, 10}. Find the symmetric difference A ∆ B.

One form of the definition is (A-B) U (B-A).

That's just the definition of symmetric difference. So your answer is wrong.

Another form is \(A\cup B \setminus A\cap B\). The modern convention is to use \(A \oplus B\) or even \( A \ominus B\), reserving \(\Delta\) for the Laplacian.

I don't provide answers to students asking for tutoring. I provide hints.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

Assumes incorrectly those are the only colas.

That's not true and even if it was true it is irrelevant. Your answer is wrong.

Your universe is composed of ten cola drinkers, possibly including people who drink RC cola but don't like Pepsi or Coke.

Math is all about those tiny little details.

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

a+b+c=1
4a+2b+c=1
9a+3b+c=3

You need to solve that system of equations for a, b, and c. Until you do so, your answer is wrong.

The sticking point for most students looking to determine the polynomial of degree \(n\) using \(n+1\) points is how to translate those points into a system of equations to be solved. Once it's framed as a system of \(n+1\) equations in \(n+1\) variables, the solution is obvious.

Oh, and you missed the deliberate error. Look closer. Try again.

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

Area = G(pi)-G(0) with G(x)=-2 cos 3x / 3
(y-2 sin 3pi/6)/(x-pi/6) = 6cos 3x

That's wrong too!

Indeed it is. Now why is it wrong? And how can it be corrected?

\(G(x)\) is clearly an antiderivative of \(g(x)\) and \(g(x)\) spends half its time below the \(x\)-axis, so should we cut the given solution in half? Why isn't that enough?

Now, find the mistake in the given equation for the tangent line at \(x=\pi/6\). No hints on this one. You either see it or you don't. Look closely.

V. Let A be the square matrix
y 2
3 x
What real values of x and y will result in matrix A having a determinant equal to 4?

xy-6=4 iff xy=10

Great! This answer is actually correct.

It wasn't really possible to provide any hint on this one short of an actual answer.

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

a, b both positive or both negative -> x=a/b >0 and x+1/x ≥ 2 -> x^2-2x+1 ≥ 0 -> (x-1)^2≥0, corollary ab<0 then a/b+b/a ≤2

That's wrong.

Lol, there's a mistake in this one, but you didn't find it. There's no mistake in the proof of the question that was posed. Written more readably:

Let \( x = a/b\). Then \( b/a = x^{-1}\).

Then \( x + 1/x \ge 2 \to x^2 +1 \ge 2x \to (x-1)^2 \ge 0 \) if \(x>0\)

The formulation shows the result can be expanded to cover the case where both \(a\) and \(b\) are negative.

The error is in the corollary. Find it. Hint: The corollary is true on a restricted domain.

VII. Prove if arbitrary n ∈ N = {0, 1, 2, ... }, then 2 | n²+ n.

if n≠0 mod 2, then n+1=0 mod 2 for all n in Z.

Wrong again.

You've surprised me. I didn't think it was possible to misread that proof. Here's the missing step.

\(n^2+n = n(n+1)\)

Obviously, there was no need to restrict the result to the natural numbers.

These are beyond trivial.

You got only one of them right. There's nothing trivial about sloppy math.

There's no such thing as proof by authority in mathematics. And your miss on that last proof doesn't bode well for any such attempt.

Try some real math.

I'd recommend you learn some "real math."

Admittedly, the question you snipped was too challenging for a novice, but that's no reason to go off in a snit.

Here's a hint: Groups have an identity element and unique inverses for all elements. So consider the cyclic subgroup \(\{g^n\}\) for any non-identity element \(g\). Show the subgroup is the entire group.

Well, it's been swell practicing insertion of LaTeX into iidb posts, but as best said by Tank Girl, "The swelling's gone down."

I'll peek in later to see if you were able to find the mistakes, but other than that, it's over and out for me.

 

[Jimmy Higgins]

Td;cu

 

[Juvenal]

Time's up, here are the solutions.

II. You poll ten people who drink cola asking each if they like Pepsi and dislike Coke, like Coke and dislike Pepsi, and possibly like both Pepsi and Coke. If 3 people like Pepsi and dislike Coke, and 4 people like Coke and dislike Pepsi, then how many of the ten people like Coke and Pepsi?

Assumes incorrectly those are the only colas.

This problem was intended to assess counting by partitions:

\( C\cup P = (C\setminus P) \,\dot\cup\, (P\setminus C) \,\dot\cup\, (C\cap P)\), hence \(| C\cap P| = |C\cup P| - |C\setminus P| - |P\setminus C| \)

with the given values where \( C\) and \(P\) are the Coke and Pepsi drinkers, respectively. But \( |C\cup P|\) can't be determined because the question didn't provide that number.

It gave the number of cola drinkers: \( |(C\cup P) \,\dot\cup\, (C\cup P)^c| \)

III. If x is any real number and a, b, and c are real numbers where f(x) = ax²+ bx + c and f(1) = 1, f(2) = 1, and f(4) = 3, then find the values of a, b, and c.

a+b+c=1
4a+2b+c=1
9a+3b+c=3

Each equation is given by replacing \(x\) and \(y\) with the values provided, except for the last equation, which inserted \( (3,3)\) instead of \( (4,3)\) in agreement with \( f(4)=3\).

IV. If x is any real number, and g(x) = 2sin(3x), then find the area under the curve of g(x) and above the x-axis over the interval 0 ≤ x ≤ π. Also, find the equation of the tangent line to the curve of g(x) when x = π/6.

Area = G(pi)-G(0) with G(x)=-2 cos 3x / 3

This question assesses the ability of a student to visualize a sine curve and note that it spends half of its time below the \(x\)-axis. The typical, harried student sees the domain \([0,\pi]\), notes the sine curve is positive there, and proceeds on, without noting the curve has been sped up, \(\omega=3\), find the antiderivative and give the above answer.

The more careful student will break the domain into regions where the graph is positive, or better, use symmetry.

The best student will see at a glance that tripling the angular speed triples the unscaled domain yielding two full humps above the \(x\)-axis, recall that each half hump has area 1, take the area of the four half-humps and scale them by 2 to match \(g(x)\) and give the answer 8 "by inspection."

(y-2 sin 3pi/6)/(x-pi/6) = 6cos 3x

This is a version of the point-slope equation of a line

\(\displaystyle \frac{y-y_0}{x-x_0}=m\)

More often, students remember this as

\( y-y_0 = m (x-x_0)\)

It was provided in the first form to allow the perceptive student to see more easily that the slope wasn't evaluated at \(x=\pi/6\), as it should have been.

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

a, b both positive or both negative -> x=a/b >0 and x+1/x ≥ 2 -> x^2-2x+1 ≥ 0 -> (x-1)^2≥0, corollary ab<0 then a/b+b/a ≤2

As above, letting \(x=a/b\), we have

\( x+1/x \ge 2 \to \\ (x-1)^2 \ge 0\) if \(x>0\)

proving the extended case where both \(a\) and \(b\) share the same sign. But if they don't, we have

\( x+1/x \ge 2 \to \\ (x-1)^2 \le 0\) because \(x<0\)

This has the unique solution \(x=1\), so the corollary is true on this restricted domain. Now here's the kicker. This also includes an error.

Find it.

 

[Jimmy Higgins]

VI. If a and b are both positive real numbers, then prove that a/b + b/a ≥ 2.

a, b both positive or both negative -> x=a/b >0 and x+1/x ≥ 2 -> x^2-2x+1 ≥ 0 -> (x-1)^2≥0, corollary ab<0 then a/b+b/a ≤2

As above, letting \(x=a/b\), we have

\( x+1/x \ge 2 \to \\ (x-1)^2 \ge 0\) if \(x>0\)

proving the extended case where both \(a\) and \(b\) share the same sign. But if they don't, we have

\( x+1/x \ge 2 \to \\ (x-1)^2 \le 0\) because \(x<0\)

This has the unique solution \(x=1\), so the corollary is true on this restricted domain. Now here's the kicker. This also includes an error.

Lowest possible value (x - 1)^2 can have is zero, if x = a/b or b/a, regardless the values of a and b, as long as they are real numbers.