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1. The number 3-540-97285-9 is obtained from a valid ISBN number by switching two
consecutive digits. Find the ISBN number. (You may write a code for this)
2. The number 0-31-030369-0 is obtained from a valid ISBN number by switching two
consecutive digits. Find the ISBN number. (The same code for question 14 should work for
this problem with a different input data too).
3. Prove by Principle of Mathematical Induction (PMI) that 3 | (4m3 + 5m) for every
nonnegative integer n
4. Prove by PMI that for every positive integer k,
1
2 *3
+
1
3* 4
+...........+
1
(k +1)*(k + 2)
=
k
2 * k + 4
5. Find a formula for 2+4+6+ ………+2m for every positive integer m and then verify your
formula by the PMI.
6. Let k ≥ 1 be an integer. Prove by PMI that 1+ k + k2 +..........+ kn =
kn+1 −1
k −1
consecutive digits. Find the ISBN number. (You may write a code for this)
2. The number 0-31-030369-0 is obtained from a valid ISBN number by switching two
consecutive digits. Find the ISBN number. (The same code for question 14 should work for
this problem with a different input data too).
3. Prove by Principle of Mathematical Induction (PMI) that 3 | (4m3 + 5m) for every
nonnegative integer n
4. Prove by PMI that for every positive integer k,
1
2 *3
+
1
3* 4
+...........+
1
(k +1)*(k + 2)
=
k
2 * k + 4
5. Find a formula for 2+4+6+ ………+2m for every positive integer m and then verify your
formula by the PMI.
6. Let k ≥ 1 be an integer. Prove by PMI that 1+ k + k2 +..........+ kn =
kn+1 −1
k −1
Question 1)
Let X be a discrete random variable with probability math function defined by:
Let X be a discrete random variable with probability math function defined by:
(D²+2DD'+D'²)z=x³
If x is a normal variable with the mean u=5 and variance (sigma square)=16, what is the probability that x is less than or equal to 6?
Math
5.1. Make a detailed critique of the philosophy of empiricism in Mathematics.
5.2. Is Mathematics dependent upon the notion of reproducibility i.e. experimentation and instantiation? Why or why not?
5.2. Is Mathematics dependent upon the notion of reproducibility i.e. experimentation and instantiation? Why or why not?
Math
4.1. How does Mill’s empiricism differ from Quine’s empiricism? Which one, to you, appears to be more appealing? Why?
4.2. What does Butterworth’s experiment about one-day old babies learning arithmetic show you? Is this evidence for or against empiricism?
4.3. Do you agree that mathematical truths derived from logical deductions are more “true” than ones based on empirical observations? Why or why not?
4.2. What does Butterworth’s experiment about one-day old babies learning arithmetic show you? Is this evidence for or against empiricism?
4.3. Do you agree that mathematical truths derived from logical deductions are more “true” than ones based on empirical observations? Why or why not?
Math
3.1. Russell’s paradox discovered by Bertrand Russell in 1901, showed that the naive set of theory of Frege leads to a contradiction.
It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those objects) that satisfy the criterion; but this assumption is disproved by a set containing exactly the sets that are not members of themselves. If such a set qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell’s paradox.
HOW WOULD YOU EXPLAIN THIS PARADOX TO YOUR STUDENTS? HOW CAN YOU ESCAPE FROM THIS PARADOX?
It might be assumed that, for any formal criterion, a set exists whose members are those objects (and only those objects) that satisfy the criterion; but this assumption is disproved by a set containing exactly the sets that are not members of themselves. If such a set qualifies as a member of itself, it would contradict its own definition as a set containing sets that are not members of themselves. On the other hand, if such a set is not a member of itself, it would qualify as a member of itself by the same definition. This contradiction is Russell’s paradox.
HOW WOULD YOU EXPLAIN THIS PARADOX TO YOUR STUDENTS? HOW CAN YOU ESCAPE FROM THIS PARADOX?
Math
2.1. Discuss the continuum hypothesis of Georg Cantor. What does Godel say about his hypothesis? What does Paul Cohen say about this hypothesis and the axiom of choice of Zermelo and Fraenkel?
2.2. Is there a set of numbers whose cardinality is greater than the cardinality of the integers but which is less than the cardinality of the reals?
2.2. Is there a set of numbers whose cardinality is greater than the cardinality of the integers but which is less than the cardinality of the reals?
Math
1. 1. Prove by simple arguments that the square root of 2 is not a rational number. What is the implication of this finding to the early Pythagoreans who claimed that all numbers are commensurable?
1.2. Discuss the “foundational issues of Mathematics”. Is Mathematics really nothing more than logic? What, in particular, would be the problem of this point of view if we consider “analysis”?
1.2. Discuss the “foundational issues of Mathematics”. Is Mathematics really nothing more than logic? What, in particular, would be the problem of this point of view if we consider “analysis”?
brad invest $1500 in an account paying 3.5% compounded monthly. How much is in the account after 7 months
" Assignmentexpert.com " is a name that MUST remember when you have a project in mathematics, even if that project is related to an advanced course!
#331389 on Nov 2022
#331389 on Nov 2022