# PLA Portfolio Assessment Course Subjects

- Forest Finance and Management (FOR-441) 3.00 s.h.
- A synthesis of principles from the biological, mathematical, physical, and social sciences applied to problems encountered in the management of forests.
- Probability (STA-321) 3.00 s.h.
- Mathematical models, sample spaces, distributions, permutations and combinations, marginal and conditional probability, discrete and continuous distributions, generating functions, multivariate distributions.
- History of Mathematics (MAT-301) 3.00 s.h.
**Course Description**

This course surveys the historical development of mathematics. Mathematical pedagogy, concepts, critical thinking and problem solving are studied from a historical perspective. The course aims at serving the needs of a wide student audience as well as connecting the history of mathematics to other fields such as the sciences, engineering, economics and social sciences. The course explores the major themes in mathematics history: arithmetic, algebra, geometry, trigonometry, calculus, probability, statistics and advanced mathematics. The historical development of these themes is studied in the context of various civilizations ranging from Babylonia and Egypt through Greece, the Far and Middle East, and on to modern Europe. Topics covered include ancient mathematics, medieval mathematics, early modern mathematics and modern mathematics.**Learning Outcomes**

Through the Portfolio Assessment process, students will demonstrate that they can appropriately address the following outcomes:- Apply mathematical techniques of problem solving.
- Describe the development of mathematics across and within civilizations around the world.
- Explain how different cultures have affected and been affected by the history of mathematics.
- Analyze and critically think about past, present and future mathematical problems.
- Recognize the distinction between formal and intuitive mathematics.
- Research historical mathematical concepts and present the conclusions of them.
- Compare and contrast the mathematical influences on the sciences, engineering, humanities and other fields.
- Present the history of mathematics in written forms.

- Mathematical Modeling (MAT-351) 3.00 s.h.
**Course Description**

This course is designed to be a bridge between the study of mathematics and the application of mathematics to various fields. It provides an overview of how the mathematical pieces of an applied problem fit together. This course also presents an investigation of meaningful and realistic problems encompassing many academic disciplines including management, economics, ecology, environmental science, sociology, and psychology. Mathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. The main goal of this course is to learn how to make a creative use of some mathematical tools, such as difference equations, ordinary and partial differential equations, and numerical analysis, to build a mathematical description of realistic problems. This includes models dealing with traffic flow, communications, energy, air pollution, currency transfer, ecosystems, inheritance, populations, bargaining, and decision making.**Learning Outcomes**

Through the Portfolio Assessment process, students will demonstrate that they can appropriately address the following outcomes:- Develop and construct appropriate models for various problems and situations.
- Analyze existing models to identify underlying assumptions and limitations.
- Apply the modeling process to translate problem situations to mathematical expressions.
- Use difference equations to model change and dynamical systems.
- Use graphical and analytic methods to fit a model to a given data set.
- Construct empirical higher-order models to fit a given data set.
- Simulate deterministic and probabilistic problems using Monte Carlo simulation.
- Develop a probabilistic model for a Markov process.
- Apply linear programming methods for constrained discrete optimization problems.
- Use graph models to solve real-world problems.
- Apply dimensional analysis in the model-building process.
- Develop and solve continuous models using differential equations.
- Use Lagrange multipliers for the optimization of continuous models.

- Math for Young Children (CDS-211) 3.00 s.h.
- This course will help prospective teachers prepare materials to develop basic mathematical concepts with conservation, seriation, and geometry. Emphasis will be placed upon the development of materials and language skills necessary for presentation of lessons.
- Introduction to Forest Mensuration (FOR-311) 3.00 s.h.
- Principles and methods of estimation and measurement of forest trees and products, singularly and in the aggregate; of trees forest products, forest stands, forest growth in time area and value. Determination by graphical and mathematical analysis of volume, growth, and valuation of wood products and other nonwood products and services of the forest through laboratory problems.
- Mathematical Logic (MAT-401) 3.00 s.h.
**Course Description**

Logic is often defined as the analysis of methods of reasoning. The mathematical logic is the study of mathematical reasoning and proof. This course starts off with the introduction to propositional calculus, the basics to the course. Then it focuses on the first-order logic and model theory. Topics covered include the metatheorems dealing with the properties of soundness, completeness, decidability, and consistency. The final part of the course is about formal number theory.**Learning Outcomes**

Through the Portfolio Assessment process, students will demonstrate that they can appropriately address the following outcomes:- Illustrate the basics of logic using truth tables.
- Utilize different axiomatic theories to prove statements logically.
- Explain the first-order languages and their interpretations.
- Discuss the various first-order theories and their properties.
- Generalize the metatheorems of soundness, completeness, decidability, and consistency.
- Define various formal number theories and properties.

- Photogrammetry (SUR-371) 3.00 s.h.
- Basic concepts of photogrammetry; basic optical, photographical, mathematical and geometric principles relevant to photogrammetry; data-acquisition systems used in photogrammetry; theory and procedures of stereoscopic mapping; overview of applications and instrumentation; map compilations using analog stereo-plotters.
- Advanced Cartography (SUR-382) 3.00 s.h.
- An introduction to cartography as a whole, cartography as a communication medium & its objectives & scope. The basic properties & characteristics of most common map projections. Mathematical derivations of some basic map projection techniques such as equal area, equidistant & conformal with major emphasis on Lambert, Mercator Transverse Mercator & Universal Traverse Mercator projections.
- Elements of Analytical Photogrammetry (SUR-474) 3.00 s.h.
- Basic mathematical models used in analytical photogrammetry; measurement and reduction of image coordinates; formulation as a least squares adjustment solution (bundle adjustment); special case of the solution; resection & intersection; treatment of normal equation systems; extended mathematical model; analytical camera calibration and determination of distortions of the photograph; analytical two-stage orientation of the stereo-pair; the analytical plotter.

*Mathematical*

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