Consider a set of logic functions \(\{ f_1(A), f_2(A), f_3(A), f_4(A)\}\) that take a proposition (\(A\)) as input which is either True or False. These functions map the truth value of the input proposition to either True or False according...
Name the two types of scientific reasoning and give an example argument for each one.
Show via Venn diagrams that the negation of a logical product ($\overline{AB}$) is equivalent to the logical sum of the negations ($\bar{A}+\bar{B}$).
Suppose some dark night a policemanwalks down a street, apparently deserted. Suddenly he hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then a gentleman wearing a mask comes crawling out through...
Show via Venn diagrams that the logical implication ($A\Rightarrow B$) is equivalent to the following expressions, \[A\bar{B} ~ \text{is false} ~,\] \[\bar{A} + B ~ \text{is true} ~,\] \[A = AB ~,\]
We have learned that the logical implication ($C\Rightarrow D$) is equivalent to the following expressions, \[C\bar{D} ~ \text{is false} ~,\] \[\bar{C} + D ~ \text{is true} ~,\] \[C = CD ~,\] Now, using the above expressions, show that if, \[(B\Rightarrow...
Consider the following Boolean algebraic expressions. Draw a Venn diagram corresponding to each one,
Problem Supposed we have observed a dataset comprised of $4975$ events with two attributes variable1 and variable2 points in this file: data.csv. Plotting these points would yield a scatter plot like the red points in the following plot, The pale...
Problem Supposed we have observed a dataset comprised of $15027$ events with one attribute variable in this file: data.csv. Plotting these points would yield a red-colored histogram like the following plot, The pale black shaded area represents the missing points...
Problem Consider the following color palettes. Which one is more appropriate for effective visualization communications with humans?
Problem Consider this dataset, usaTemperatureHistory.txt, which contains the global land temperature of the earth from 1743 to 2013 at every monthly resolution. As stated in the file, temperatures are in Celsius and reported as anomalies relative to the average global...
Problem Consider this dataset, 1880_2020.csv, which contains the global land and ocean temperature anomalies of the earth from January 1880 to June 2020 at every month. As stated in the file, temperatures are in Degrees Celsius and reported as anomalies...
Problem Consider this CSV dataset containing the durations of a set of astrophysical events (T50 and T90), their corresponding 1-sigma uncertainties (T590err, T90err), the event IDs (Trigger) and the starting time of the events (T90Start) with respect to some reference...
Problem Consider the following plot. Explain the types of $x-$ and $y-$ axes of this plot. What type of mathematical function would best describe the initial (seemingly linear) phases of the three blue, yellow, and red curves in this plot?...
Problem Integration by midpoint rule: The idea of the Midpoint rule for integration is to divide the area under a curve $f(x)$ into $n$ equal-sized rectangles. The height of the rectangle is determined by the value of $f$ at the...
Consider the following set of Fortran module files: Constants_mod.f90, JaggedArray_mod.f90, String_mod.f90, Math_mod.f90. (These files are actually part of the ParaMonte library). These modules depend on each other: Math_mod uses Constants_mod and String_mod, String_mod uses Constants_mod and JaggedArray_mod, JaggedArray_mod uses Constants_mod,...
Problem How can I install Intel Parallel Studio on Windows? Solution The Intel Parallel Studio provides a wide variety of High-Performance numerical libraries and tools, most importantly, the Intel Fortran and C/C++ compilers. However, its installation on Windows systems, in...
Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...
Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...
Problem Consider this dataset, Drand.mat, which contains a set of random numbers. Write a sctipt that computes the mean of this sample via the Least-Sum-of-Squares method. For this, you will need to use a funtion minimizer in the language of...