Homework
Math 2984 - Fall 2017
Intro to Mathematical Problem Solving
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HW001: Estimate the square root of 2017:
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HW002: Report circle closest in area to a given square:
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HW003: Evaluate a formula for water density as a function of temperature:
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HW0035: Evaluate a formula for the normal probability function:
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HW004: Evaluate a formula estimating the weight of a child given its age.
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HW005: Evaluate a formula involving fractions.
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HW0055: Evaluate an 8 digit binary number, using IF().
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HW006: Given 3 numbers, how many are distinct?
Use IF/ELSE.
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HW007: Given 3 numbers, can they represent the sides of a triangle?
Use IF/ELSEIF/ELSE and a Boolean variable.
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HW008: For I from 0 to 10, print I, square of I, square root of I,
using a FOR loop.
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HW009: For I from 100 to 200, sum the square of each I,
using a FOR loop.
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HW0091: Using a FOR loop and the RAND function, estimate the
average distance between two random points in the unit square.
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HW0092: Using a FOR loop and the RAND function, estimate the
probability that a "random" quadratic equation will have real roots.
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HW010: Print the first 100 prime numbers, using a WHILE loop
and ISPRIME().
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HW011: Print integers 123 UP to 255 by 17's, then 255 DOWN to 123 by 17'2,
using FOR loops with an increment.
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HW0115: Every year 30% of Californians move out, and 10% of US moves in.
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HW012: Rewrite a positive number x in scientific notation, using WHILE loops.
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HW013: Print factors of an integer, using a WHILE loop.
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HW014: Print multiplication tables for numbers between P and Q,
using nested FOR loops.
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HW015: Print a pyramid of stars using nested FOR loops.
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HW016: Print a table of greatest common divisors for numbers between P and Q,
using nested FOR loops and the GCD() function.
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HW017: What month does day N occur in? Use a vector of month lengths.
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HW018: Compute a version of the Fibonacci sequence with different starting
values.
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HW019: Compute a version of the Fibonacci sequence that adds the previous
three values.
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HW020: Count the number of derangements, knowing the first two values
and a recurrence relation.
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HW021: Count the number of subsets of size K from a set of size N,
using a recurrence relation.
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HW022: Estimate the arithmetic-geometric mean using recurrence.
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HW023: Estimate the area under y=humps(x) for x between 0 and 1,
using a FOR loop.
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HW024: Estimate the probability that calling rand() three times
gives us three numbers that could be the lengths of the sides
of a triangle.
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HW025: Estimate the probability that breaking a unit stick
in two random places gives us three pieces that can form
a triangle.
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HW026: Given a Month/Day date like 4/10, return the
number of days since the beginning of the year.
You need a vector to store the length of each month.
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HW027: Estimate the value of an alternating infinite
series with monotonically decreasing entries, using WHILE.
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HW028: Pay your grocery bill at the automatic checkout, using WHILE.
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HW029: Approximate the golden ratio, by computing entries in a
sequence, until the difference between two consecutive entries is
small enough.
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HW030: If a penny is dropped down a well that reaches the center of
the earth, when will it hit the bottom?
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HW031: In what year will the population of reporters be smaller
than the population of wind turbine technicians?
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HW032: When will a typical child weigh more than 1000 pounds,
according to the Theron formula?
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HW033: Create a plot of 24 values that record monthly transatlantic
air traffic from January 1949 to December 1950.
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HW034: Create a plot that shows the first five Chebyshev polynomials
of the second kind.
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HW035: Create a plot of the letters "VT", joined or separate,
and filled in with a color.
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HW036: Draw a checkerboard.
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HW037: Draw a face using filled ellipses.
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HW038: Write a function to compute the perimeter of a triangle.
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HW039: Write a function to shrink a triangle by a factor s.
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HW040: Write a function to compute the area of a quadrilateral,
using a function that computes the area of a triangle.
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HW041: Write a script that seeks a zero of the Wallis function
y=x^3-2x-5..
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HW042: Write a script that seeks three zeros of the cubic function
y=816*x^3 - 3835*x^2 + 6000*x - 3125.
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HW043: Write a script that determines the value of the golden
ratio by seeking a solution of the equation x=1/(1+x).
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HW044: Write a function that uses logical vectors and find()
to analyze a vector.
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HW045: Write a function that estimates how many times a random
walk will visit the square labeled 0.
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HW046: Write a function that tracks the frequency of each possible
score when tossing N dice M times and creates a bin plot of the results.
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HW047: Read a PNG file containing a grayscale image
of Saturn, change to white all the pixels in a
5-pixel wide strip along the border of the image,
and save the modified image to a JPG file.
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HW048: Read a PNG file containing a grayscale image of
a scene from the movie "Casablanca";
copy Ingrid Bergman's head and use it to replace
the heads of Humphrey Bogart and Dooley Wilson;
save the image as "bergman3.jpg".
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HW049: Read a JPG file which is a photograph of a person. Make a new
JPG file which only displays pixels that closely match a particular shade.
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HW050: Create a contour plot of a function that represents a "valley".
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HW051: Create a surface plot of a function that exhibits four
deep depressions.
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HW052: Use the contour() function to draw a family of ellipses.
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HW053: Compute the cumulative probabilities for an event with
outcomes that have unequal likelihoods.
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HW054: Use a transition model to simulate how 800 students shift
between three dormitories.
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HW055: Use a transition model to simulate how 1000 customers switch
car insurance policies each year.
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HW056: Read a list of edges describing a graph and create a
corresponding adjacency matrix.
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HW057: Using the RISK adjacency matrix, determine the maximum distance
from Western Australia to any region on the game board.
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HW058: Fill out the SPOT survey for our class.
