Data Scientists

• Apply classical solution techniques to differential equation models of physical systems
• Construct partial differential equation models for physical systems
• Contextualize partial differential equation models of physical systems

• Independently research mathematical concepts
• Synthesize pertinent mathematical background material

• Apply group theoretic concepts to solve mathematical problems
• Apply group theoretic concepts to the natural sciences

• use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.
• set up and solve second order, constant coefficient differential equations that arise from physical systems such as mass-spring systems and RLC circuits.  In addition, students will have a strong intuition of the phenomenon of resonance.
• employ Laplace transforms to solve differential equations with discontinuous forcing terms.

• Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.
• Explain the relation between the time and frequency domains, and apply techniques for converting from one domain to another.

Work with the applications of geometric transformations in the sciences

• Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.
• Construct finite-difference schemes in order to approximate solutions to differential equations and analyze their order of approximation

Apply the techniques of multiple integration and partial derivatives to applied problems

• Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions
• Demonstrate knowledge of relationships between exponents and logarithms and their derivatives

Apply number theoretic techniques to cryptography

• Solve simple differential equations focusing on topics in economics.
• Apply basic linear algebra to economic problems.

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Utilize quantitative methods to analyze linear and non-linear systems of differential equations

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

• Use mathematical software to approximate solutions of biological models
• Construct model equations from a description of a biological system

• Implement a program that uses an array to solve a problem.
• Write, compile and execute a complete program for a given problem.
• Implement code that reads information from a file.

• Create an interpreter or compiler from a Backus-Naur specification. (iv)
• Make practical use of Regular Expressions

Write rigorous correctness proofs for algorithms.

• Demonstrate the ability to analyze algorithms to interpolate data with polynomials.
• Employ the appropriate numerical technique to approximate a solution of an initial value problem, boundary value problem, or partial differential equation, with careful consideration of initial or boundary data.

use numerical schemes to find approximate solutions to initial value problems utilizing mathematical software such as Matlab or Mathematica.

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Apply differential and integral calculus techniques to trigonometric functions, exponential functions, logarithmic functions and the inverses of these functions

Work with the applications of geometric transformations in the sciences

Employ and analyze a prescribed method to find a root of a nonlinear equation (with knowledge of the strengths and weaknesses of the approach);

Perform in-order, pre-order, post-order, and possibly Euler traversals of a tree.

Program a memory management simulation.

• Summarize the professional report in an oral presentation
• Independently research mathematical concepts
• Write a professional report adhering to scholarly standards
• Synthesize pertinent mathematical background material

Work with the applications of geometric transformations in the sciences

Visualize models graphically

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Utilize qualitative methods to analyze linear and non-linear systems of differential equations

Program a memory management simulation.

Use mathematical software to approximate solutions of biological models

Model a physical signal by using mathematical functions, and solve the equations when excited by an arbitrary function.

Visualize models graphically

• Sketch the qualitatively valid graph of the derivative of a function presented graphically (formulas not used)
• Demonstrate the role of continuity in evaluating limits graphically and numerically

Interpret output from statistical software correctly

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

• Utilize qualitative methods to analyze linear and non-linear systems of differential equations
• Illustrate changes in the solution structure via a bifurcations diagram

Compute areas between graphs of function

Demonstrate a facility with curves given parametrically

Work with the applications of geometric transformations in the sciences

Interpret output from statistical software correctly

Use mathematical software to approximate solutions of biological models

Implement code that reads information from a file.

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

Program a memory management simulation.

• Understand and use the heap data structure and its applications in sorting and priority queue.
• Analyze the asymptotic performance of algorithms.

• Interpret output from statistical software correctly
• Apply non-parametric statistical tests

Implement code that reads information from a file.

Demonstrate the ability to analyze algorithms to interpolate data with polynomials.

• Apply group theoretic concepts to solve mathematical problems
• Apply group theoretic concepts to the natural sciences

Understand sampling theorem, upsampling and downsampling.

Apply non-parametric statistical tests

Analyze a communication system and measure a performance in terms of probability of

Investigate properties of a statistical estimator based on characteristics of bias, efficiency, consistency and sufficiency

Perform reductions and simplifications of linear models

• Write a professional report adhering to scholarly standards
• Independently research mathematical concepts

Write a professional report adhering to scholarly standards

Independently research mathematical concepts

Apply basic linear algebra to economic problems.