This class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Learning and Understanding Mathematical Concepts in the Areas of Water Distribution and Water Treatment. From College of the Canyons.

Table of Contents
Section 1: Unit Dimensional Analysis
Section 2: Geometric Shapes
Section 3: Density and Specific Gravity
Section 4: Chemical Dosage Analysis
Section 5: Weir Overflow Rate
Section 6: Water Treatment Math Detention Time
Section 7: CT Calculations
Section 8: Pressure, Head Loss, and Flow
Section 9: Well Yield, Specific Capacity, and Drawdown
Section 10: Horsepower and Efficiency
Section 11: Per Capita Water Usage
Section 12: Blending and Diluting
Section 13: Scada and the Use of mA
Section 14: Water Utility Management

Students learn about the differences between types of water (surface and ground), as well as the differences between streams, rivers and lakes. Then, they learn about dissolved organic matter (DOM), and the role it plays in identifying drinking water sources. Finally, students are introduced to conventional drinking water treatment processes.

Students act as engineers contracted by NASA to create water filtration devices that clean visible particulates from teacher-prepared "dirty water." They learn about the worldwide need for potable water and gain appreciation for why water quality is an important issue for people on Earth as well as on the International Space Station. Working in groups, students experience the entire engineering design process, including a read-aloud book about the water cycle; a visiting water engineer presentation; their own online research about filter methods and designs; group brainstorming of designs (using ordinary household materials); filter construction and testing; redesign and retesting; lab book documentation of their notes, research, plans and results; and a summary poster presentation at a mini-engineering fair. Two design planning worksheets, a poster layout suggestion sheet and a grading rubric are provided.

Student teams design and then create small-size models of working filter systems to simulate multi-stage wastewater treatment plants. Drawing from assorted provided materials (gravel, pebbles, sand, activated charcoal, algae, coffee filters, cloth) and staying within a (hypothetical) budget, teams create filter systems within 2-liter plastic bottles to clean the teacher-made simulated wastewater (soap, oil, sand, fertilizer, coffee grounds, beads). They aim to remove the water contaminants while reclaiming the waste material as valuable resources. They design and build the filtering systems, redesigning for improvement, and then measuring and comparing results (across teams): reclaimed quantities, water quality tests, costs, experiences and best practices. They conduct common water quality tests (such as turbidity, pH, etc., as determined by the teacher) to check the water quality before and after treatment.

Students leach organic matter from soil to create a water sample with high dissolved organic matter content (DOM), and then make filters to see if the DOM can be removed. They experience the difficulties of removing DOM from water, and learn about other processes that might make DOM removal more effective.

After watching a short online video that recaps the enormous scale of accumulating plastic waste in our oceans, student teams are challenged to devise a method to remove the most plastic microbeads from a provided commercial personal care product—such as a facial cleanser or body wash. They brainstorm filtering methods ideas and design their own specific procedures that use teacher-provided supplies (coffee filters, funnels, plastic syringes, vinyl tubing, water, plastic bags) to extract the microplastics as efficiently as possible. The research and development student teams compare the final masses of their extracted microbeads to see which filter solutions worked best. Students suggest possible future improvements to their filter designs. A student worksheet is provided.

Student teams learn how water filtration systems that use nanoparticles and nanotechnology can remove organic compounds from water. First they learn about the role nanoparticles play in water filtration. Then they are introduced to the basics of nanoparticles and nanotechnology, focusing on the impacts and benefits this innovative technology has on our daily lives. Using methylene blue and methyl orange solutions, students test for the efficiency of photocatalytic nanoparticles to sanitize water. They expose a solution sample of water and methyl orange (the microbe indicator) with their newly-made water sanitation filters under UV light (sunlight) to activate the photocatalytic properties of three specific nanoparticles. They visually compare them with control samples to determine the best photocatalytic nanoparticle to sanitize water.

Osmosis is the passive movement of water across a semi permeable membrane. It occurs in the opposite direction to diffusion of ions. Water moves from a region of low solute concentration and therefore high water concentration to a region of high solute concentration and low water concentration.

Students are introduced to the growing worldwide environmental problems that stem from plastic waste. What they learn about microplastics and the typical components of the U.S. water treatment process prepares them to conduct three engaging associated activities. During the lesson, students become more aware of the pervasiveness and value of plastic as well as the downstream pollution and health dangers. They learn how plastic materials don’t go away, but become microplastic pollution that accumulates in water resources as well as human and other animal bodies. They examine their own plastic use, focusing on what they discard daily, and think about better ways to produce or package those items to eliminate or reduce their likelihood of ending up as microplastic pollution. A concluding writing assignment reveals their depth of comprehension. The lesson is enhanced by arranging for a local water treatment plant representative to visit the class for Qs and As. In three associated activities, students design/test microplastic particle filtering methods for commercial products, create mini wastewater treatment plant working models that remove waste and reclaim resources from simulated wastewater, and design experiments to identify the impact of microplastics on micro-invertebrates.

Students experience the steps of the engineering design process as they design solutions for a real-world problem that could affect their health. After a quick review of the treatment processes that municipal water goes through before it comes from the tap, they learn about the still-present measurable contamination of drinking water due to anthropogenic (human-made) chemicals. Substances such as prescription medication, pesticides and hormones are detected in the drinking water supplies of American and European metropolitan cities. Using chlorine as a proxy for estrogen and other drugs found in water, student groups design and test prototype devices that remove the contamination as efficiently and effectively as possible. They use plastic tubing and assorted materials such as activated carbon, cotton balls, felt and cloth to create filters with the capability to regulate water flow to optimize the cleaning effect. They use water quality test strips to assess their success and redesign for improvement. They conclude by writing comprehensive summary design reports.

Student teams practice water quality analysis through turbidity measurement and coliform bacteria counts. They use information about water treatment processes to design prototype small-scale water treatment systems and test the influent (incoming) and effluent (outgoing) water to assess how well their prototypes produce safe water to prevent water-borne illnesses.

This course covers the general principles of separation by equilibrium and rate processes. Topics include staged cascades and applications to distillation, absorption, adsorption, and membrane processes. Phase equilibria and the role of diffusion are also covered.

In this lesson, students will explore the causes of water pollution and its effects on the environment through the use of models and scientific investigation. In the accompanying activities, they will investigate filtration and aeration processes as they are used for removing pollutants from water. Lastly, they will learn about the role of engineers in water treatment systems.

Students learn about water quality testing and basic water treatment processes and technology options. Biological, physical and chemical treatment processes are addressed, as well as physical and biological water quality testing, including testing for bacteria such as E. coli.

Students are asked to design methods to filter water using ordinary materials, while also considering their designs' material and cost efficiencies. They learn about the importance of water and its role in our everyday lives. They come to understand what must occur each day so that they can have clean water.

In this lesson, the students will conduct an investigation to purify water. Students will engineer a method for cleaning water, discover the most effective way to filter water, and practice conducting a scientific experiment.