Mathematics

- Mathematics Major - No Emphasis
- Mathematics Major - Actuarial Science Emphasis
- Mathematics Major - Teaching Grades 5-8 Emphasis
- Mathematics Major - Teaching Grades 6-12 Emphasis
- MS Degree - Mathematics Major

The goals for the BS program are to produce graduates who:

**Goal 1**: Have demonstrated the ability to do and learn mathematics.

The student earning a BS in math can demonstrate conceptual and procedural understanding of:- The concepts of calculus, including single and multivariable calculus, and is able to identify and apply these relationships within a real-world context, including the use of appropriate technology
- The concepts of algebra, both Linear and Abstract, including topics such as matrices, linear transformations, characteristic polynomials, eigenvalues and eigenvectors, vector spaces, systems of linear equations and elementary theory of groups, rings, and fields
- The concepts of a wide variety of mathematics including area such as Probability and Statistics, Real Analysis, Discrete Mathematics, Differential Equations, Geometry, and Numerical Analysis

**Goal 2**: Have demonstrated the ability to apply mathematics to real world problems.

The student earning a BS in math can solve a variety of problems set in a real-world context, in particular:

- Routine problems that involve one or two concepts from a single area of mathematics and not more than a two-step standard reasoning process
- Nonroutine problems that involve several concepts from a variety of areas of mathematics and several steps of reasoning
- Applied problems that may be composed of several routine and nonroutine components

**Goal 3**: Are prepared to become productive employees or succeed in graduate school.

The student earning a BS in math has a diverse background in mathematics that has prepared the student to demonstrate mastery of the learning outcomes and objectives specified above:- By conducting independent research and present the results at state, regional, and national conferences
- By exhibiting the skills necessary to successfully find employment in an area related to mathematics
- By exhibiting the prerequisite competencies for acceptance and successful completion of a graduate degree in mathematics or a related field

The goals forActuarial Science Emphasis are to produce graduates who:

**Goal 1**: Have demonstrated the ability to do and learn mathematics.

The student earning a BS in math can demonstrate conceptual and procedural understanding of:- The concepts of calculus, including single and multivariable calculus, and is able to identify and apply these relationships within a real-world context, including the use of appropriate technology
- The concepts of algebra, both Linear and Abstract, including topics such as matrices, linear transformations, characteristic polynomials, eigenvalues and eigenvectors, vector spaces, systems of linear equations and elementary theory of groups, rings, and fields
- The concepts of a wide variety of mathematics including area such as Probability and Statistics, Real Analysis, Discrete Mathematics, Differential Equations, Geometry, and Numerical Analysis

**Goal 2**: Have demonstrated the ability to apply mathematics to real world problems.

The student earning a BS in math can solve a variety of problems set in a real-world context, in particular:

- Routine problems that involve one or two concepts from a single area of mathematics and not more than a two-step standard reasoning process
- Nonroutine problems that involve several concepts from a variety of areas of mathematics and several steps of reasoning
- Applied problems that may be composed of several routine and nonroutine components

**Goal 3**: Are prepared to become productive employees or succeed in graduate school.

The student earning a BS in math has a diverse background in mathematics that has prepared the student to demonstrate mastery of the learning outcomes and objectives specified above:- By conducting independent research and present the results at state, regional, and national conferences
- By exhibiting the skills necessary to successfully find employment in an area related to mathematics
- By exhibiting the prerequisite competencies for acceptance and successful completion of a graduate degree in mathematics or a related field

**Goal 4A**:

The student earning a BS with an emphasis in Actuarial Science has relevant knowledge in mathematics and business to:

- Demonstrate mastery of the learning outcomes and objectives specified in the syllabi for Exams 1/P and 2/FM jointly administered by the Casualty Actuarial Society and Society of Actuaries
- Demonstrate mastery of the learning outcomes and objectives required for Validation through Educational Experience (VEE) credits in Economics, Corporate Finance, and Applied Statistics
- Obtain a summer internship as a student and employment in the actuarial profession after graduation

The goals for the Teaching Grades 5-8 Emphasis are to produce graduates who:

**Goal 1**: Have demonstrated the ability to do and learn mathematics.

The student earning a BS in math can demonstrate conceptual and procedural understanding of:- The concepts of calculus, including single and multivariable calculus, and is able to identify and apply these relationships within a real-world context, including the use of appropriate technology
- The concepts of algebra, both Linear and Abstract, including topics such as matrices, linear transformations, characteristic polynomials, eigenvalues and eigenvectors, vector spaces, systems of linear equations and elementary theory of groups, rings, and fields
- The concepts of a wide variety of mathematics including area such as Probability and Statistics, Real Analysis, Discrete Mathematics, Differential Equations, Geometry, and Numerical Analysis

**Goal 2**: Have demonstrated the ability to apply mathematics to real world problems.

The student earning a BS in math can solve a variety of problems set in a real-world context, in particular:

- Routine problems that involve one or two concepts from a single area of mathematics and not more than a two-step standard reasoning process
- Nonroutine problems that involve several concepts from a variety of areas of mathematics and several steps of reasoning
- Applied problems that may be composed of several routine and nonroutine components

**Goal 3**: Are prepared to become productive employees or succeed in graduate school.

The student earning a BS in math has a diverse background in mathematics that has prepared the student to demonstrate mastery of the learning outcomes and objectives specified above:- By conducting independent research and present the results at state, regional, and national conferences
- By exhibiting the skills necessary to successfully find employment in an area related to mathematics
- By exhibiting the prerequisite competencies for acceptance and successful completion of a graduate degree in mathematics or a related field

**Goal 4E**: Are prepared to teach mathematics to diverse populations.

The student earning a BS with an emphasis in Mathematics Teaching 5-8 or 6-12 can demonstrate mastery of the learning outcomes and objectives specified KSDE*Regulations and Standards for Kansas Educators*for the specific grade level:- By exhibiting the ability to teach mathematics to pre-college students
- By exhibiting an understanding of undergraduate mathematics sufficient to teach in a pre-college setting
- By exhibiting a mastery of currently accepted mathematical pedagogical knowledge

The goals for the Teaching Grades 6-12 Emphasis are to produce graduates who:

**Goal 1**: Have demonstrated the ability to do and learn mathematics.

The student earning a BS in math can demonstrate conceptual and procedural understanding of:**Goal 2**: Have demonstrated the ability to apply mathematics to real world problems.

The student earning a BS in math can solve a variety of problems set in a real-world context, in particular:

- Applied problems that may be composed of several routine and nonroutine components

**Goal 3**: Are prepared to become productive employees or succeed in graduate school.

The student earning a BS in math has a diverse background in mathematics that has prepared the student to demonstrate mastery of the learning outcomes and objectives specified above:- By exhibiting the skills necessary to successfully find employment in an area related to mathematics

**Goal 4E**: Are prepared to teach mathematics to diverse populations.

The student earning a BS with an emphasis in Mathematics Teaching 5-8 or 6-12 can demonstrate mastery of the learning outcomes and objectives specified KSDE*Regulations and Standards for Kansas Educators*for the specific grade level:- By exhibiting the ability to teach mathematics to pre-college students
- By exhibiting an understanding of undergraduate mathematics sufficient to teach in a pre-college setting
- By exhibiting a mastery of currently accepted mathematical pedagogical knowledge

The goals for the MS program are to produce graduates who:

**Goal 1**: Have demonstrated the ability in core areas of mathematics necessary in advanced graduate programs.

The student earning an MS in math can demonstrate conceptual and procedural understanding of:- The concepts of analysis, in terms of both the real line and the complex plane, and is able to apply these concepts.
- The concepts of algebra, both Linear and Abstract, including topics such as linear transformations, characteristic polynomials, eigenvalues and eigenvectors, vector spaces, and advanced theory of groups, rings, and fields.

**Goal 2**: Have demonstrated the ability to apply mathematics to real world problems and conduct independent research beneficial in obtaining professional employment in industry, including the actuarial sciences.

The student earning an MS in math has a diverse background in advanced mathematics and can demonstrate conceptual and procedural understanding of:

- The concepts in a specialized area of mathematics tailored to the student’s individual career goals.
- The techniques of mathematical research by conduct independent research and presenting the results in a comprehensive written format.

**Goal 3**: Are provided a broader and deeper mathematical background beneficial to teachers of mathematics, both at the 6-12 and community college level.

The student earning an MS in math can demonstrate a diverse background in advanced mathematics that has prepared the student to:- Comprehend the mathematics taught in middle school and high school at a deeper level and understand how the topics in various areas of mathematics correspond and complement each other.
- Understand how the mathematics taught at the high school and community college level relates to the advanced study of mathematics.

Physics

- Physics Major (Bachelor of Science Degree)
- Physics Education Emphasis
- Physics Major (Master of Science Degree)
- Materials Science Major (Master of Science Degree)

The American Physical Society and the American Association of Physics Teachers publish nationally accepted standards that the PSU Physics Department takes as “best practice” for our BS Degree in Physics. These have been incorporated into our student learning outcomes.

**Goal 1:**All physics graduates must have broad factual knowledge and thorough competency in the fundamentals of physics and the skills necessary to construct basic scientific knowledge of material phenomena. They must:- Objective 1(a): Demonstrate a depth of understanding in the fundamentals kinematics, dynamics, energy and momentum conservation, waves, heat and thermodynamics. Focus: PHYS 100, 104, 130, 510, 699.
- Objective 1(b): Demonstrate a depth of understanding in the fundamentals of electricity, magnetism, optics, special relativity, atomic structure, and properties of radiation. Focus: PHYS 101, 105, 131, 512, 516, 612, 699.
- Objective 1(c): Demonstrate the ability to collect, analyze and interpret scientific data. Focus: PHYS 130, 131, & 530.

**Goal 2:**All physics graduates must have the ability to communicate effectively. They must:- Objective 2(a): Be able to write a well-organized, logical, scientifically-sound research paper or laboratory report. Focus: PHYS 130, 131, 530, 691.
- Objective 2(b): Be able to present a well-organized, logical, scientifically-sound, and audience- appropriate oral report on a scientific topic. Focus: PHYS 691.

The American Physical Society and the American Association of Physics Teachers publish nationally accepted standards that the PSU Physics Department takes as “best practice” for our BS Degree in Physics. These have been incorporated into our student learning outcomes.

**Goal 1:**All physics graduates must have broad factual knowledge and thorough competency in the fundamentals of physics and the skills necessary to construct basic scientific knowledge of material phenomena. They must:- Objective 1(a): Demonstrate a depth of understanding in the fundamentals kinematics, dynamics, energy and momentum conservation, waves, heat and thermodynamics. Focus: PHYS 100, 104, 130, 510, 699.
- Objective 1(b): Demonstrate a depth of understanding in the fundamentals of electricity, magnetism, optics, special relativity, atomic structure, and properties of radiation. Focus: PHYS 101, 105, 131, 512, 516, 612, 699.
- Objective 1(c): Demonstrate the ability to collect, analyze and interpret scientific data. Focus: PHYS 130, 131, & 530.

**Goal 2:**All physics graduates must have the ability to communicate effectively. They must:- Objective 2(a): Be able to write a well-organized, logical, scientifically-sound research paper or laboratory report. Focus: PHYS 130, 131, 530, 691.
- Objective 2(b): Be able to present a well-organized, logical, scientifically-sound, and audience- appropriate oral report on a scientific topic. Focus: PHYS 691.

**Goal 3:**All pre-service physics teachers must demonstrate their ability to set-up and introduce a physics laboratory exercise and be able to effectively tutor students to complete the exercise in a formal setting.

**Goal 1:**To produce graduates with factual knowledge and mathematical skills necessary to solve complex physics problems.- Objective 1(a): Demonstrate deep understanding and solve fundamental problems in Electricity and Magnetism using Maxwell’s Equations including (Focus: PHYS 812):

- 1(a).1 electric field, potential and charge density calculations
- 1(a).2 method of images
- 1(a).3 solutions of Laplace’s equation in different coordinate systems with specified boundary conditions
- 1(a).4 multi-pole expansion
- 1(a).5 Green's function expansion
- 1(a).6 dielectric medium and displacement field
- 1(a).7 magnetic field calculations

- Objective 1 (b): Demonstrate deep understanding and solve fundamental problems in quantum mechanics using (Focus: PHYS 816):

- 1(b).1 matrix theory to solve spin and simple harmonic oscillator problems
- 1(b).2 techniques with angular momentum, spherical harmonics, and tensors
- 1(b).3 perturbation methods

- Objective 1(c): Demonstrate deep understanding of the principles analytical mechanics using (Focus: PHYS 810):

- 1(c).1 Newton’s 2nd Law and conservation theorems applied to multiple-body problems,
- 1(c).2 Lagrange’s equations as applied the two-body problem and constraint problems,
- 1(c).3 Hamilton’s equations as applied to conservative systems, and
- 1(c).4 Canonical Transformations and Hamilton-Jacobi Theory.

- Objective 1(a): Demonstrate deep understanding and solve fundamental problems in Electricity and Magnetism using Maxwell’s Equations including (Focus: PHYS 812):
**Goal 2:**All physics graduates must engage in scientific research and have the ability to communicate the process and results of the research effectively.

- Objective 2(a): Be able to write a well-organized logical, scientifically sound research paper, scientific report, or grant proposal. Focus: PHYS 890, 891, 893.
- Objective 2(b): Be able to present effectively a well-organized, logical, scientifically sound, and audience-appropriate oral report on a scientific topic. Focus: PHYS 890, 891, 832.

**Goal 3:**All physics graduates with an Option II – Teaching emphasis will broaden and deepen their science background and be able to effectively guide others in learning science.

- Objective 3(a): Be able to guide and encourage secondary school students in research projects in the physical sciences. Focus: PHYS 882.
- Objective 3(b): Be able to summarize and compare central issues and debates of philosophers of science. Focus: PHYS 760.

**Goal 1:**To produce graduates with in-depth knowledge of materials science, which involves connections between the underlying structure of a material and its physical and chemical properties.- Objective 1(a): Demonstrate understanding and solve problems in Nanophysics and Thin Films which deal with physical and electronic properties in reduced dimensions, film deposition techniques, and characterizations.
- Objective 1(b): Demonstrate understanding and solve problems in Solid State Physics and Electronics which involve physical and electronics properties of crystals and semiconductors, including crystal structure, bonding, doping, and electronic properties semiconductors.
- Objective 1(c): Write computer programs in Python for modeling and predicting materials behavior without doing the actual experiments.
- Objective 1(d): Demonstrate understanding and problem-solving skills in the physical chemistry of polymers, mechanics of composite materials, and testing.
- Objective 1(e): Learn working principles and hands-on experience on many state-of-an-art instruments such as scanning electron microscope, x-ray diffraction, atomic force microscopy, Raman spectroscopy, thermal analyzer, electrochemistry, and many more.

**Goal 2:**All materials science graduate students must engage in research, follow new developments in their field via attending colloquiums/conferences, have the ability to design and communicate the process and results of the research effectively.

- Objective 2(a): Write a well-organized, logical, scientific report or thesis based on original research performed
- Objective 2(b): Present a well-organized, logical, report or thesis on original research performed
- Objective 2(c): Develop skills to design and perform new experiments
- Objective 2(d): Learn basics of instruments and hands-on experience on many state-of-the-art instruments
- Objective 2(e): Learn industrial standards for materials testing
- Objective 2(f): Get experience on industrially/state/federal funded projects