# STEM

## Mathematics Courses

## Computer Science Courses

## Sciences Courses

#### STEM at Middlesex

The Science, Technology, Engineering and Math (STEM) Division is made up of the Mathematics, Science, and Computer Science departments. These departments have in common an approach to the solution of problems through mathematical analysis and an emphasis on the scientific method, i.e. empirical observation leading to the formulation of general mathematical laws which can be used to predict new observations.

In the classroom, STEM courses at Middlesex emphasize not only subject-specific knowledge, but also critical thinking, problem solving, and effective communication of scientific and mathematical ideas. Hands-on activities and laboratory investigations illustrate both the concepts and process of problem solving. Students use technology to see principles in action and to learn to make conclusions about the world based on evidence. We expect students to be prepared for and engaged in classroom activities. While the challenge of learning may vary among our students, we believe that a student’s understanding is strengthened by both independent and collaborative contemplation of and grappling with new concepts and problems. Teachers work with students to develop their skills and individual interests.

These tools attain their greatest power when students learn how to approach problems by integrating mathematical modeling, creative thought, previous mathematical experience and scientific inquiry, to clearly see their way to a solution that might be generalized to all problems of that nature. Technology has an important part to play in both the presentation of material and the students’ ability to solve problems.

The STEM Division is committed to developing students’ abilities to investigate and solve 21st century problems. Students may earn a certificate for completing an Experience with Problem-solving, Reasoning, and Technology (ExPRT) through designated ExPRT courses in the Division or through approved extra-curricular projects or contests. Each ExPRT consists of open-ended problems that require the equivalent of several course periods of work. These problems require students to perform research and analyze data, and they provide students with a variety of opportunities to incorporate technology. Each ExPRT requires collaboration and culminates with students presenting their solutions in both oral and written form. Extra-curricular endeavors through which an ExPRT Certificate can be earned should be undertaken in consultation with the ExPRT Committee.

All courses offered in this Division confer distributional credit to members of Classes I and II, but only those courses so designated in the descriptions confer credit toward departmental requirements in laboratory science or mathematics. Advanced Placement courses are available to students in Class I or Class II or with the permission of the Department.

#### The Science Department

The goals of the Science Department at Middlesex are to promote in our students an understanding of the natural world and to develop in them the ability to engage in scientific inquiry. We aim to prepare future scientists, engineers, and medical professionals for the next phase of their training, while also providing non-scientists with skills and habits that will serve them well regardless of their field of study. We expect that our students, after studying science at Middlesex, are informed citizens, critical consumers of scientific data, and savvy users of technology.

We value both depth and breadth in our courses; we believe that a complete science education includes both understanding of the fundamentals of current scientific thought as well as detailed exploration and comprehensive mastery of particular concepts of interest. To that end, we encourage students at Middlesex to progress through introductory courses in all three major disciplines of science, biology, chemistry, and physics, before exploring further areas of interest in Applied Science or Advanced Placement courses.

Students are encouraged to take Biology, or in some instances Chemistry, in Class IV; Chemistry, or in some instances Physics, in Class III; and Physics in Class II. The department offers a variety of advanced topics courses for students who have met the lab science requirement. Advanced Placement courses are available to qualified students in Class II or Class I who have completed the appropriate prerequisite courses and with the permission of the Department.

Biology, Chemistry, Physics and Environmental Science are full-year courses. These courses completed in a single academic year confer credit for laboratory science. Semester long advanced science courses confer distributional credit, but do not confer credit for laboratory science.

##### Science Courses: 2019-2020

In the case of over enrollment in *Applied Science *courses, preference will be given to members of Class I.

SCIENCE 40. *Applied Science: Ecology and Conservation Biology. Fall. Mrs. Irwin. 4 meetings weekly.* *Preference given to Class II and III**.* The human population is experiencing a radical demographic shift. According to the United Nations, 55% of the world’s population lived in urban areas in 2018, and that percentage could increase to 68% by 2050. This unprecedented change in human settlement patterns presents unique and pressing environmental issues. This course will examine the intersection of human population and ecosystems through the lens of conservation biology and urban ecology. Students will apply principles of conservation biology to explore the current mass extinction and consider the ethics, economics, policy, and design of conservation management systems. The course will then examine the field of urban ecology to look specifically at how natural systems interact with the urban environment and how urban ecologists are studying and attempting to control those interactions.

SCIENCE 41. *Applied Science: Astronomical Tools for Answering Really Big Questions. Spring. Ms. May. 4 meetings and 1 evening observation session weekly. Open to Class II and III. *This course will study the necessary requirements for life beyond Earth, the possibility of extraterrestrials, and the size, scope, and formation of the universe. The tools for these conversations will be those of astronomy, and students will be expected to participate in evening laboratory exercises. Students will study astronomical instruments (telescopes, satellites), astronomical information (electromagnetic waves), and astronomical principles. Students should expect to use their algebra skills at times in this class. They should also expect to do presentations on their knowledge, as well as take tests and quizzes, including a final exam. THIS COURSE WILL NOT BE OFFERED IN 2019-2020.

SCIENCE 42. *Applied Science: CSI: Middlesex – An Introduction to Forensic Science. Spring. Mr. Bishop. 3 meetings weekly. Preference given to Class I and II. ExPRT Certificate eligible*

**.**This course examines the science and practical techniques behind crime scene investigation. Judging by the numerous TV shows about solving mysteries through careful analysis of material clues, forensics is a hot topic. This interdisciplinary course will incorporate a basic understanding of principles of chemistry, physics, biology, geometry, and physiology with a practical use of the scientific method to help reconstruct criminal events. Topics to be covered include fingerprinting, toxicology, serology, blood spatter, and hair, fiber, and DNA analysis. Lab activities will accompany each topic. Students will be evaluated by lab reports, semester long projects, and class attendance and participation.

SCIENCE 43. *Applied Science:* *Brain* *and Behavior. **Spring. Mrs. Sheff. 4 meetings weekly. Preference given to Class I and II.* This semester-long course concentrates on an introduction to the nervous system with an emphasis on the neural mechanisms underlying human and animal behavior. We will focus on the relationship between biology and behavior paying attention to the biological basis of sensory and motor systems such as vision and voluntary movements, and higher mental processes such as memory, learning, language, and attention. Finally the course will look at the consequences that disorders of the nervous system have on behavior and discuss methods of treatment for these disorders. Those taking the course should have an interest in the constantly growing field of neuroscience. Students will be evaluated by examinations, papers, and class participation.

SCIENCE 44. *Applied Science: Biotechnology. Spring. Mr. Whitt. 4 meetings weekly. Open to Class II and III. *This course examines the myriad of technological advances that have enhanced the study of the life sciences. Biotechnology is the study of biology through technical applications; these new and evolving technologies have furthered our own understanding of many different living systems. Common technologies from this field are utilized in medical, agricultural, industrial, environmental, and research applications. In this course, students will examine the most common tools utilized by researchers, including gene manipulation, production of biological molecules, gene mapping, and examining current events, among others. Students will engage with the various topics through lecture, classroom discussion, and laboratory activities. In this course, students will be evaluated by classroom participation, lab reports, and unit assessments.

SCIENCE 45. *Applied Science: Advanced Astronomy. Fall. Ms. May. 4 meetings and 1 evening observation session weekly. Preference given to Class I and II. ExPRT Certificate eligible. *This semester-long astronomy course begins with a survey of the night sky. We will then move on to describe and explain astronomical phenomena on both the scale of the very near and the very, very far. Exact topics will depend on the interests of the class and the celestial objects visible during the semester. Possible areas of exploration include tides, lunar phases, the space program, our solar system (including planets and our Sun), stellar evolution (including red giants, supernovae, neutron stars, and black holes), galaxy formation, cosmology (including the big bang and fate of the universe), and extraterrestrial life. In every topic of study, students are expected to write about their understanding and present their knowledge to their classmates. Frequent class presentations should be expected. Students in this course will, through required weekly nighttime observing sessions, learn the basics of naked-eye astronomy and become proficient in the use of our rooftop telescopes in the Middlesex Observatory. Opportunities to use the 18-inch Centurion telescope housed in the dome will also be provided.

SCIENCE 46. *Applied Science: Environment, Society, and Technology. Spring. Dr. Mylon. 4 meetings weekly. Preference given to Class I and II.* This course will address how human activity has affected the environment, and how technologies, public policies and lifestyle choices can also impact it. We will use the lens of the scientist to discover the interconnectedness of important environmental systems. Topics will include: the atmosphere, water and its resources, elements important to both the environment and global economies, and energy. After completion, students will have developed literacy with respect to the environment and current environmental issues. Students will be assessed through a combination of homework assignments, tests and projects.

SCIENCE 47. *Applied Science: Biomedical Ethics. Fall. Mrs. Sheff. 4 meetings weekly. Preference given to Class I and II. Distributional credit in STEM or the Humanities*

**.**The twenty-first century promises to be filled with medical and technological advances that not only will enhance the quality of life, but will also generate a myriad of ethical questions and controversies. Our present definitions and qualities of life from beginning to end will be sorely tested and debated. The overlap between science and religion, science and ethics, and science and the legal system will become even more blurry, and it is important as future consumers, patients, and citizens of the world that we be as informed as possible. This course will examine as many of the issues as possible: reproductive technologies, genetics, enhancement, organ transplantation, human experimentation and research ethics, end of life ethics, and health care, among others. We will read essays and articles, as well as listen to podcasts and debates to inform our own classroom discussion and debate. Students will be evaluated on stance papers, debates, classroom participation, and a final bioethics paper on a topic of their choosing.

SCIENCE 48. *Applied Science: Engineering. Fall. Mr. Bishop. 4 meetings weekly. Preference given to Class I and II. ExPRT Certificate eligible*

**.**This course is based upon the

*Engineer Your World*curriculum designed by the Cockrell School of Engineering at the University of Texas at Austin. The course engages students in authentic engineering practices and inspires them to embrace an engineer’s habits of mind. Collaborative, student-directed projects build resilient problem-solving skills and empower students to think like engineers, to adopt engineering processes, and to pursue engineering disciplines for the betterment of our world. Students discover the design process by creating cameras for people with disabilities. They reverse engineer a crank flashlight to think about how someone else designed it – and how they could do it better. Students uncover the challenges and opportunities of working together to collect, analyze, represent, and argue from data. The course culminates as they use these skills to redesign a building in an earthquake zone.

SCIENCE 49.* Applied Science: Robotics. Fall. Dr. McDonald. 4 meetings weekly.**Open to Class I and II. ExPRT Certificate eligible. *Robots are programmable machines. They are our agents, building and working in industry at repetitive tasks or in dangerous places we cannot go. Equipped with sensors, these machines can gather data and respond to changes in the world around them. Combined with artificial intelligence, these machines can explore the surface of Mars, disarm explosives, learn to perform delicate surgery or respond to danger faster than we can on our own. Robotics is about improving our quality of life and pushing the limits of what humans can do. This hands-on, minds-on course introduces the field of robotics through a series of projects that challenge us to build, design, and code robots. Students will work as engineers, individually and in teams, to think creatively and critically as they tackle real world problems and prototype solutions. Students will be assessed on their contributions, successes and reflections during each step of the problem-solving process. By the end of this course, students will have learned the basics of this exciting branch of engineering and they will have a deeper insight into their own problem-solving styles and talents.

##### Biology Courses: 2019-2020

BIOLOGY 10. *Biology. Fall. The Department. 5 meetings weekly. Open to all classes.* Biology 10 and Biology 11/12 constitute a full year course. An introductory course which attempts to develop an understanding of the basic principles governing the living world, to instill in the student a perspective of himself or herself as a living organism, and to develop skills in experimental technique and scientific reasoning. Students continue on to Biology 11 or Biology 12 in the spring semester.

BIOLOGY 11. *Biology. Spring. The Department. 5 meetings weekly. Open to all classes. Prerequisite: Biology 10. *A continuation of Biology 10, with an emphasis on the concepts of genetics, molecular biology, evolutionary theory and the major regulatory and locomotive systems of the body.

BIOLOGY 12. *Honors Biology. Spring. The Department. 5 meetings weekly. Open to all classes. Prerequisite: Biology 10 and Permission of the Department*. Intended for students with a strong record of accomplishment in Biology 10. This course will more rigorously approach and develop the topics offered in Biology 11 and will cover additional material. Topics include genetics, molecular biology, biotechnology, evolution and major body systems.

BIOLOGY 20. *Advanced Placement Biology. Year. Dr. Magee. 5 meetings weekly. Prerequisite: Biology, Chemistry, and Permission of the Department. Students will be ranked and admitted to the course based on their performance in previous science courses (biology, chemistry). Preference will be given to members of Class I and II and students who have completed physics*. This challenging full year, college-level biology course is offered as a second-year course in biology for extraordinary science students, especially those who have an interest in the fields of medicine or biological research. The two main goals of the course are to help students develop a conceptual framework for modern biology and an appreciation of science as a process. The ongoing knowledge explosion in biology makes these goals even more challenging. This course follows the AP Biology syllabus published by the College Board and covers major topics in the fields of biochemistry, cellular and molecular biology, classical and modern genetics, development, animal systems, ecology and evolution. Inquiry based labs are an integral part of this course, as are nightly reading assignments and homework assignments that are designed to have the students apply the concepts learned in class. This course uses an eBook as a primary resource as well as several websites and iPad apps to further explore the topics. This course prepares students for the Advanced Placement Examination in Biology.

##### Chemistry Courses: 2019-2020

CHEMISTRY 10. *Chemistry. Fall. The Department. 5 meetings weekly. Open to all classes.* Chemistry 10 and Chemistry 11/12 constitute a full year course. **Students must have completed or be concurrently enrolled in Math 31 in the spring semester in order to complete a year of chemistry.** This course explores a core of principles that organizes the whole of chemistry. Coverage will include topics such as atoms and molecules, nuclear chemistry, prototypical reactions, periodic properties of the elements, bonding and the mole. Emphasis will be placed on progressing from the general to the specific and from the simple to the complex as we explore current understanding in the field of chemistry. Instruction will include both lecture and laboratory, and effort will be made to engage the student in the learning process. In addition to reading and problem sets, there will be in-class collaborative learning assignments, computer-based tutorials, and online resources.

CHEMISTRY 11. *Chemistry. Spring. The Department. 5 meetings weekly. Open to all classes. Prerequisite: Chemistry 10 and concurrent enrollment in Math 31 or higher*. This course is a continuation of Chemistry 10 and will cover stoichiometry, gas laws, chemical kinetics, chemical equilibrium, and acid base chemistry. Emphasis will be placed on understanding chemical concepts that underlie the topics discussed. A mathematical approach to the topics will be supported with online tutorials, practice problem sets, and in-class group work. Laboratory work will be designed to provide students with hands-on examples of the topics covered.

CHEMISTRY 12. *Honors Chemistry. Spring. The Department. 5 meetings weekly.Open to all classes. Prerequisite: Chemistry 10, concurrent enrollment in Math 31 or higher and Permission of the Department.* This course is a continuation of Chemistry 10 and will cover stoichiometry, gas laws, chemical kinetics, chemical equilibrium, acid base chemistry, oxidation reduction reactions, and electrochemistry. This course is designed for students with a strong record of accomplishment in Chemistry 10, who are prepared for a mathematically more rigorous approach to the study of chemistry. Students will be responsible for making their own connections between what they are taught and greater chemical principles at large. Laboratory work is designed to reinforce and expand a student’s understanding of the topics covered.

CHEMISTRY 20. *Advanced Placement Chemistry. Year. Dr. Schaeberle. 5 meetings weekly. Prerequisite: Chemistry, Physics, Math 49 and Permission of the Department. Students will be ranked and admitted to the course based on their performance in previous science courses (chemistry, physics) and Math 49. Preference will be given to members of Class I and II and students who have completed biology, chemistry and physics*. Equivalent to first year college chemistry, this course is designed for students intending to concentrate their studies in science, engineering, or medicine. This course follows the AP Chemistry syllabus published by the College Board and covers the advanced topics include quantum theory and atomic structure, biochemistry, chemical equilibria, kinetics, thermodynamics, electrochemistry, spectroscopy, and nuclear chemistry. Inquiry based labs are an integral part of this course and will include quantitative and qualitative analysis. This course prepares students for the Advanced Placement Examination in Chemistry.

##### Physics Courses: 2019-2020

PHYSICS 10. *Physics. Fall. The Department. 5 meetings weekly. Open to Classes I, II, and III. Prerequisite: completion or concurrent enrollment in Math 31*. **ExPRT Certificate eligible.** Physics 10 and Physics 11/12 constitute a full year course. This course introduces the fundamental ideas of physics, emphasizing conceptual explanations and basic algebraic problem solving. The course starts with a study of waves and sound and then transitions to the basics of the electromagnetic spectrum and the behavior of light. It then examines electrostatics, electricity and simple circuits. Finally, the course will investigate forces as it prepares students to examine the objects in motion around them.

PHYSICS 11. *Physics. Spring. The Department. 5 meetings weekly. Open to Classes I, II, and III. Prerequisite: Physics 10.* This course is a continuation of Physics 10 and will employ hands-on activities and projects to study the concepts of motion, free fall, forces, vectors, projectiles and energy. Problem solving and conceptual explanations continue to be emphasized. If time allows the topics of universal gravity, magnetism and electromagnetism will be explored.

PHYSICS 12. *Honors Physics. Spring. The Department. 5 meetings weekly. Open to Classes I, II, and III. Prerequisite: Physics 10 and Permission of the Department.* This course is a continuation of Physics 10 and uses the tools of algebra and basic trigonometry to enhance conceptually rigorous analyses. The course starts with a description of motion (kinematics and vectors). Using these tools, the concepts of forces, conservation laws, energy, momentum, and rotation are applied to real world problems. After mechanics, the class turns to topics of electricity and magnetism. Other topics such as modern physics (nuclear physics, atomic physics and special relativity), fluid dynamics, and thermodynamics may be included depending on the pace and interests of the class.

PHYSICS 20. *Advanced Placement Physics 1: Algebra-Based. Year. Dr. Erickson. 5 meetings weekly. Open to Classes I, II, and III. Prerequisite: completion or concurrent enrollment in Math 32 and a semester average of 90 or better in Chemistry 11 or a semester average of 86 or better in Chemistry 12. Preference will be given to members of Class I and Class II. In the case of over enrollment students will be ranked and admitted into the course based on their performance in chemistry and Math 31*. This challenging college-level introductory physics course is offered as a first-year course in physics for extraordinary science students. The emphasis is both conceptual understanding and mathematical problem solving. This course follows the AP Physics 1 syllabus published by the College Board, covering topics of Newtonian mechanics (including rotational dynamics and angular momentum); work, energy, and power and mechanical waves and sound. It will also introduce electric circuits. Inquiry based labs are an integral part of this course and will include quantitative and qualitative analysis. This course prepares students for the Advanced Placement Examination in Physics 1: Algebra-Based.

PHYSICS 25. *Advanced Placement Physics 2: Algebra-Based. Year. Dr. Mylon. 5 meetings weekly. Open to Classes I, II, and III. Prerequisite: Biology, Chemistry, Physics 12 or higher and Permission of the Department*. This challenging college-level introductory physics course is offered as a second-year course in physics and covers fluid mechanics; thermodynamics; electricity and magnetism; optics and atomic and nuclear physics. Inquiry based labs are an integral part of this course and will include quantitative and qualitative analysis. This course prepares students for Advanced Placement Examination in Physics 2: Algebra-Based.

PHYSICS 30. *Advanced Placement Physics C. Year. Ms. May. 5 meetings weekly. Open to Classes I and II. Prerequisite: Successful completion of Physics 20, and either completion of Math 52 or completion or concurrent enrollment in Math 55 and Permission of the Department. In the case of over enrollment, students will be ranked and admitted into the course based on their performance in Physics 20 and Math 50 courses. *This calculus-based physics course is a challenging and detailed examination of two central parts of classical physics: mechanics and electricity and magnetism. The course is intended for students with a strong interest in science and mathematics. AP Physics C aims to instill in students a deeper understanding of major topics in first-year physics, with more derivations, more difficult problems, and more sophisticated mathematics. This course prepares students for both Advanced Placement Examinations in Physics C (Mechanics, and Electricity and Magnetism).

##### Environmental Science Courses: 2019-2020

ENVIRONMENTAL SCIENCE 20. *Advanced Placement Environmental Science. Year. The Department. 5 meetings weekly. Prerequisite: Biology, Chemistry, and Permission of the Department.* Students will be ranked and admitted to the course based on their performance in previous science courses (biology, chemistry). Preference will be given to members of Class I and II and students who have completed physics.This course provides a conceptual basis for understanding the environment by presenting the principles of ecology and using them to analyze environmental issues. Environmental science is interdisciplinary in terms of science and in terms of its consideration of the role of social, cultural and economic factors. The relationship of environmental problems to resources, population, pollution, and policy making will be investigated and opposing views of major issues and policies will be discussed and evaluated. Some field work in the Estabrook Woods and at Bateman’s Pond will be part of the course. Students will use a textbook and current reading in newspapers and periodicals will also be required. This course prepares students for the Advanced Placement Examination in Environmental Science.

#### The Mathematics Department

The course offerings in mathematics are designed to provide students with a deep and thorough knowledge of the essential framework of mathematics. Students are encouraged to think in a quantitative fashion in order to model aspects of their experience and the world around them. The essentials of algebra, geometry, and elementary functions provide some of the tools which allow them to think in informed ways about aspects of life such as: growth and decay, periodic phenomena, change, and chance.

Our intention is to have students assume responsibility for the mathematics they explore—to understand theorems that are developed, to be able to use techniques appropriately, to know how to test results for reasonability, to learn to use technology appropriately, and to welcome new challenges whose outcomes are unknown.

Through support and encouragement, teachers at Middlesex seek to expose and develop the potential of each student. To this end we aim to support where needed, challenge when appropriate, inculcate sound reasoning skills and encourage articulate communication of mathematical ideas. We hope our students will experience success and satisfaction in mastering a body of knowledge that is fundamental to their education. Beyond this, we very much wish to impart a sense of the utility, beauty and power of mathematics.

The Mathematics Department assumes new students will arrive having studied some algebra. To help the department determine the appropriate course, a placement test will be sent to all entering students. Students who will benefit from a review of first year algebra will be placed in Math 12; those with stronger algebra backgrounds will be placed in Math 21 or higher.

Courses 12 through 32, each one-semester long, comprise the core of the mathematics curriculum. Middlesex uses a variety of approaches in its mathematics courses with a particular focus on problem solving. We expect that, by the end of the core courses, a student will have a full grasp of the fundamental tools of algebra, and confidence in tackling problems which are both challenging and original. Technology is used extensively throughout our curriculum and is a tool we expect students to use effectively.

Advancement in math courses is based on mastery of the material in a course. Any student who achieves a grade below 70 in Math 21 or 31 must remain at that level and repeat the course. The department may recommend that a student repeat a level after receiving a semester grade between 70 and 73. Should a student taking a repeat course fail to make satisfactory progress in the repeat course, the student will be required to take a summer school course approved by the School.

Middlesex offers a rich variety of math courses beyond the required sequence. It is our belief that students are well served by seeing branches of mathematics other than the purely algebraic. These 40 – level courses may be taken in any order at any time after completion of Math 32. Students interested in taking an Advanced Placement course in either calculus or statistics (or economics) should note that Math 49 is a prerequisite for these courses.

##### Math Courses: 2019-2020

MATH 12. *Intermediate Algebra. Fall. The Department. 5 meetings weekly. *This course is a review and extension of the topics of a first year algebra course. It is designed for those students who have had an introduction to algebra and who would benefit from a review of the material. Topics covered include linear equations and their graphs, exponents and roots, functions, matrices, and systems of equations.

MATH 21. *Algebra and its Functions. Fall, Spring. The Department. 5 meetings weekly. *This one-semester course is designed to strengthen and extend first year algebraic knowledge. Topics will include a review of linear functions, absolute value, inequalities, and quadratic functions. Students will use graphing calculators to explore concepts.

MATH 22. *Geometry. Fall, Spring. The Department. 5 meetings weekly and a lab. Prerequisite: The equivalent of a full year of algebra.* This one-semester course will consist of an inductive study of the principles and properties of Euclidean geometry. Definitions will be established and theorems will be developed, verified, and proved. The treatment of proof will center on congruence of triangles and properties of quadrilaterals. Geometric software will be used to help explore and amplify concepts. **Note: New students who have not yet studied geometry will be placed into geometry in the SPRING semester**.

MATH 31. *Advanced Algebra. Fall, Spring. The Department. 5 meetings weekly*. This one-semester course extends knowledge of algebra and functions to include the graphs, behaviors, applications and properties of a variety of functions. Students will work extensively with exponential and logarithmic functions. Students will investigate transformations, compositions, and the inverses of function.

MATH 32. *Pre-calculus: Trigonometry. Fall, Spring.The Department. 5 meetings weekly.* The circular functions will be examined in depth in this one-semester course, which includes trigonometric functions, identities, inverse trigonometric functions, applications to triangles and vectors.

**The following courses are open to all students who have completed their mathematics requirements through the level of Math 32.**

MATH 40. *Advanced Topics in Mathematics – Discrete Mathematics. Fall, Spring. The Department. 4 meetings weekly.* This one-semester course will cover topics in mathematics which do not depend upon concepts of infinity. Topics which naturally fall into this category and will be considered in this course are linear programming, matrix algebra, sets and counting, probability and the mathematics of finance.

MATH 41. *Advanced Topics in Mathematics – Mathematical Modeling. Fall. The Department. 4 meetings weekly.* ** ExPRT Certificate eligible.** In this project-based course, students will work individually and collaboratively to formulate and analyze mathematical models used to solve complex problems. Examples might include: developing best use of elevators in a high-rise building, or using data to determine distinctions between two similar insect species. Solutions and results of students’ work will be summarized in written reports and presentations. Students will participate in a mathematical modeling contest in November.

MATH 42. *Advanced Topics in Mathematics – Coding Mathematical Algorithms. Fall. The Department. 4 meetings weekly. *This course serves as an introduction to the principles of computer coding, requiring logic and problem-solving skills as students work towards the goal of producing a computer game. Participants will learn to manipulate graphics and animations, use code to solve math problems, and develop algorithms to achieve desired behavior for characters and objects in their games. No prior programming experience is required, though students should be comfortable working independently and solving problems creatively.

MATH 43. *Advanced Topics in Mathematics – Quantitative Analysis. Fall. The Department. 4 meetings weekly. ExPRT Certificate eligible*

**.**This course teaches students the principles of programming spreadsheet applications, financial modeling, and securities valuation. The first part of the course focuses on the basics of programming spreadsheets, building a three-statement operating model of a company, and discounted cash flow valuation. The second part of the course focuses on financial ratios, public and acquisition comparables, the leveraged buyout model, and an introduction to equity options valuation and graphs. The course concludes with students presenting a detailed valuation of a public company and a buy/sell recommendation.

MATH 44. *Advanced Topics in Mathematics* – *Problem Solving. Spring. The Department. 4 meetings weekly. ExPRT Certificate eligible. *This course focuses on mathematical problem solving. Everyday situations can lead an inquisitive problem solver to profound and far-reaching mathematical principles. Discussions accompanying the problems reinforce important techniques in discrete mathematics, and the solutions – which require verbal arguments – show that proofs and careful reasoning are at the core of doing mathematics. In addition, we will learn that asking good questions is just as important to the progress of mathematics as answering questions. This course will serve interested students seeking to improve their problem-solving knowledge and know-how.

MATH 45. *Advanced Topics in Mathematics – Advanced Geometry. Spring. The Department. 4 meetings weekly. *Geometry is a rich and beautiful field of mathematics, to which high school students typically only receive a cursory introduction through a standard Euclidean geometry course. Through a combination of problem-solving and formal proof, students will explore additional topics in Euclidean geometry, three-dimensional shapes and surfaces, and analytical geometry. Time permitting, we may even abandon Euclid’s fifth postulate and consider the mindboggling worlds of non-Euclidean geometry. Computer software will be utilized for visualization and to enhance the concepts studied. Students in this course will be expected to collaborate as they delve into these fascinating topics.

MATH 46. *Advanced Topics in Mathematics – Calculus. Spring. The Department. 4 meetings weekly.* This one-semester course is designed to give an intuitive introduction to the techniques of calculus and to the sorts of problems with which elementary calculus deals. It is hoped that this less formal presentation will attract students interested in continuing mathematical study short of the Advanced Placement sequence in calculus. **Note: Students who enroll in Math 46 may not take Math 50 or Math 52**

MATH 47. *Advanced Topics in Mathematics – **Applied Statistical Reasoning. Spring. The Department. 4 meetings weekly. *This course introduces the principles of statistical reasoning using a student-friendly approach that emphasizes the entire statistical process in a motivating sports context, making it a unique and powerful way to learn about statistics. This course will begin with an analysis of quantitative and qualitative variables, test hypothetical claims, as well as look at different measures of location and variability. The second half of the course will look at the use of statistics in how it drives the current use of analytics across all major sports and see how regression can be used to make predictions. Can a swimsuit make you faster? Who should I draft for my fantasy baseball team? Applied Statistical Reasoning examines fascinating questions about sports and life by investigating the underlying statistical questions which students can analyze through data and simulations in order to draw conclusions.

MATH 48. *Advanced Topics in Mathematics – Statistics. Fall, Year. The Department. 4 meetings weekly.* **ExPRT Certificate eligible if taken for the full year**.This course covers many of the major topics of descriptive statistics. In the fall, topics covered will include displays of sample data, measures of center and spread, probability, discrete random variables and normal distributions. A student may elect to take only the fall class or they may continue the study throughout the year. The emphasis of the spring semester will be inferential statistics. The topics will be partially determined by the interests of the class or instructor. **Note: Students who enroll in Math 48 may not take Math 51.**

MATH 49. *Advanced Topics in Mathematics – Pre-calculus. Fall, Spring.The Department. 5 meetings weekly.* This one-semester course is designed to prepare students for calculus, and the focus will be on problem solving using mathematical models to represent real world situations. After a review of elementary functions, with particular attention to polynomial and rational functions, students will investigate conic sections by way of parametric equations and, finally, examine sequences and series. **This course is a prerequisite for ALL AP level math courses.**

MATH 50. *Differential Calculus. Spring. The Department. 5 meetings weekly. Prerequisite: Math 49 and Permission of the Department. Students may not take Math 50 concurrent with or subsequent to Math 46. *This in-depth course in calculus will develop and explore the concept of limit and then progress to the development of the derivative. Derivatives of polynomial, trigonometric, and exponential functions and their applications to graphing, velocity, acceleration, max-min problems, and related rates will be studied.

MATH 51. *Advanced Placement Statistics. Year. The Department. 5 meetings weekly. Prerequisite: Math 49 and Permission of the Department. Students may not take Math 51 concurrent with or subsequent to Math 48. *During the first semester, data descriptive statistics, data collection and probability are the foci of this course. During the second semester, the emphasis is on inferential statistics. Topics include confidence intervals and tests of significance for means and proportions, power and error, chi-squared tests and inference for regression. This course prepares students for the Advanced Placement Examination in Statistics.

MATH 52*. Advanced Placement Calculus AB. Year. The Department. 5 meetings weekly. Prerequisite: Math 49 and Permission of the Department. Students may not take Math 52 concurrent with or subsequent to Math 46.* This is a yearlong course in both differential and integral calculus which covers the syllabus of the AB Advanced Placement Examination. From the development of the definition of derivative, to its application to a series of related problems, this investigation of differential calculus will cover all topics in which the rate of change of a function is the primary interest. The second semester will then begin an extensive investigation in integral calculus, focused primarily on assorted techniques of integration. The tool of integration will then help the student think about assorted questions of area, length, volume and related physical problems.

MATH 55.* Advanced Placement Calculus BC. Year. The Department. 5 meetings weekly. Prerequisite: Math 50 and Permission of the Department. Students may not take Math 55 after taking Math 52. *This year-long course covers the syllabus associated with the BC Advanced Placement Examination. The development of the idea of accumulation and the closely associated topic of the area will motivate much of the discussion in the first semester of this course. After the development of the integral and various techniques of integration we will investigate a series of related physical problems dealing with growth, decay, volume, and length. The course will conclude with a study of analytic geometry, polar coordinates, differential equations and infinite series.

MATH 60. *Multivariable Calculus. Fall. The Department. 4 meetings weekly. Prerequisite: Completion of the Math 55 syllabus.* After a brief review of the topics in analytic geometry, polar coordinates, and parametric equations, we will study vectors in 2-space and 3-space. The topics will include tangent and normal vectors, curvature, dot product, cross product, curves and planes in 3-space, and quadric surfaces. THIS COURSE WILL NOT BE OFFERED IN 2019-2020.

MATH 61. *Introduction to Linear Algebra, Part I. Fall. The Department. 4 meetings weekly. Prerequisite: Completion of the Math 55 syllabus*. This is a course in the study of linear, or vector, spaces and the structure of linear mappings between such spaces. Topics in this course include vector spaces, matrices, linear transformations, and solutions of systems of linear equations.

MATH 62. *Linear Algebra, Part II. Spring. The Department. 4 meetings weekly. Prerequisite: Math 61. * In this continuation of the study begun in Math 61, we’ll study eigenvalues, eigenvectors, and the diagonalization of matrices, along with applications to differential equations.

MATH 65. *Vector Calculus. Spring. The Department. 4 meetings weekly. Prerequisite: Math 60*. This course will be a study of multivariable calculus with attention paid to partial derivatives, multiple integrals and their applications, Stokes’ and Green’s theorems, and the related underpinnings of vector theory. THIS COURSE WILL NOT BE OFFERED IN 2019-2020.

#### Computer Science at Middlesex

Computer Science extends beyond simply typing code into a computer. In an ever more interconnected world, understanding the Internet, data abstraction and storage, encryption, web security, and the global impact of technology has become exceedingly important. Thus, the Middlesex Computer Science Department aims to educate students about the principles of computer science and advance the problem solving abilities of its students through courses that emphasize the development and implementation of creative algorithms. The true essence of programming lies in creatively approaching a problem, designing a solution, and then translating that solution into executable code. While instruction in the higher level programming courses primarily focuses on Java, students will develop an intuitive understanding of programming language structure and object-oriented programming, which allows them to learn new languages with ease.

The department recognizes that students’ interests in computer science will vary widely, and thus the department attempts to meet these varying interests by providing two entry-points into the computer science curriculum at Middlesex. A two-semester course sequence (Computer Science 20-21) exists for students seeking an introduction to computational thinking, algorithms, and fundamental programming concepts. **This course sequence is designed for students desiring a general understanding of their technological world and the fundamentals of programming, but that do not intend to pursue computer programming in their future academic career.**

**Students seeking to develop extensive computer programming skills and pursue college-level coursework, should begin their computer science study with Computer Programming 25**, which in conjunction with Computer Programming 55 also covers the material on the A Level Advanced Placement Computer Science examination. These two courses are equivalent to the first semester of computer science as taught at virtually all universities and colleges that use Java in their coursework for computer science majors. Upon completion of Computer Programming 55, students can continue their study of algorithms, computer organization, data structures, and discrete mathematics topics applicable to computer science by enrolling in the Computer Programming 61-62 course sequence. Students having completed these courses should possess the ability to use functional and object-oriented programming algorithms, constructs, and data structures to solve advanced computational problems. Additionally, they will be able to analyze algorithm and program efficiency with respect to both execution time and space requirements.

For the truly sophisticated students, advanced topics in computer science can be studied upon completion of Computer Science 62. Students should note, however, that completion of four semesters of history during their Middlesex careers is a graduation requirement, which should be taken into consideration as they plan their computer science course progression.

*The Computer Science 20-21 sequence is intended for students interested in learning more about exciting new ideas in computer science, but who are not necessarily interested in developing extensive programming skills.*

##### Computer Science Courses: 2019-2020

COMPUTER SCIENCE 20. *Principles of Computer Science. Fall. Ms. Heitmiller. 4 meetings weekly. Prerequisites: Math 22, or Math 21 and Permission of the Department. In the case of over enrollment, preference will be given to students in Class I or II, and students will be ranked by performance in Math 21, Math 22, and other core math courses.* This course introduces students to the foundational concepts of computer science where they will explore how computing and technology can impact the world. Students will explore the infrastructure of the Internet, the processes involved in data communication, storage of digital information, big data, digital privacy, as well as an introduction to object oriented programming. This course emphasizes creative problem solving and real-world applications that connect the material being studied to students’ everyday lives.

COMPUTER SCIENCE 21.*Computational Thinking. Spring. Ms. Heitmiller. 4 meetings weekly. Prerequisite: Computer Science 20. ExPRT Certificate eligible.Students that have completed Computer Programming 25 or higher may not enroll in Computer Science 21*. In this course, students will be given the opportunity to apply the concepts studied in Computer Science 20 and develop their programming abilities using Java; topics covered will include loops, methods, conditionals, logic gates, and parameters. Students will also undertake a variety of research projects where they explore how computing affects current societies, economies, and culture. Students intending to take the Advanced Placement examination in Computer Science Principles should enroll in Computational Thinking and participate in the weekly workshop offered by the Department during the spring semester.

**Note: Students that complete Computer Science 21 may not enroll in Computer Programming 25.***The following Computer Programming courses are intended for students interested in developing extensive programming skills. Students interested in a general overview of computer science are encouraged to enroll in Computer Science 20 instead.*

COMPUTER PROGRAMMING 25. *Programming in Java. Fall. **The Department.** 4 meetings weekly. Open to members of Classes I or II and to members of Classes III and IV with Permission of the Department. Prerequisites: Math 22, Math 31. Students that have completed Computer Science 21 may not enroll in Computer Programming 25*

**.**This course teaches the fundamentals of object-oriented programming using Java. Topics covered will include computer number systems, data types, selection constructs, loops, methods, Strings, and object encapsulation. The course stresses the understanding of problem solving in terms of algorithmic development.

COMPUTER PROGRAMMING 55. *Advanced Placement Computer Science A. Spring. **The Department.** 5 meetings weekly. Prerequisite: Computer Science 21 or Computer Programming 25, and Permission of the Department. Students will be ranked and admitted based upon their performance in Computer Science 21 or Computer Programming 25. ExPRT Certificate eligible. *In this course, students examine and write larger and more complex programs consisting of multiple classes. It will consider style and expression, structured coding, modularization, implementation, testing, and maintenance of software. Related topics include arrays, the construction of classes, inheritance, polymorphism, and recursion. Measuring algorithm efficiency will be considered with particular emphasis on sorting and searching. Prepares students for the A Level Advanced Placement Examination in Computer Science.

COMPUTER PROGRAMMING 60. *Advanced Computer Programming Topics. Fall, Year. The Department. 4 meetings weekly. Prerequisite: Computer Programming 55 with Permission of the Department. ExPRT Certificate eligible*. Especially qualified students may study advanced topics such as multimedia and web design and production, networking, algorithm design and analysis, theory of computation, programming languages, computer architecture, software development, iOS or Android app development, or operating systems. Students in this course will be expected to do a considerable amount of independent study. May be taken as either a one-semester (fall only), or yearlong course. Students enrolled in this course will participate in the American Computer Science League contests. THIS COURSE WILL NOT BE OFFERED IN 2019-2020.

COMPUTER PROGRAMMING 61. *Discrete Mathematics and Data Structures. Fall. Mr. Pillai. 4 meetings weekly. Prerequisites: Computer Programming 55 and Permission of the Department*. This course introduces discrete mathematics topics necessary for advanced study of computer science such as predicate logic, Boolean algebra, digital electronics, bit-string flicking, regular expressions, mathematical induction, and graph theory. Additionally, after an introduction to file manipulation and graphical user interfaces using Java, there will be an in-depth examination of the data structures in the Java Collections library. Collaborative skills to work in teams to complete larger programming projects will also be developed. Students enrolled in this course will participate in the American Computer Science League contests.

COMPUTER PROGRAMMING 62. *Advanced Data Structures and Algorithms. Spring. Mr. Pillai. 4 meetings weekly. Prerequisite: Computer Programming 61 and Permission of the Department. ExPRT Certificate eligible. *This advanced course in data structures will begin with a detailed discussion of problem solving with the following abstract data types: iterators, linked lists, stacks, queues, trees, graphs, maps, tables, and priority queues. Big-Oh algorithm analysis and proving the correctness of recursive functions will also be considered. Time permitting, students will also be taught how to use the typesetting language LaTeX. The course concludes with the completion of a large programming group project. Students enrolled in this course will participate in the American Computer Science League contests.

COMPUTER PROGRAMMING 70. *Seminar in Advanced Computer Programming. Fall, Year. The Department. 4 meetings weekly. Prerequisites: Computer Programming 62 and Permission of the Department. ExPRT Certificate eligible*. This open-ended course will focus on topics of interest to students who have completed the programming courses through Computer Programming 62. Possible areas of study might include (but are not limited to) assembly language, software design and development, app development, databases, or artificial intelligence. Large scale, collaborative programming projects will be a primary focus of this course, and students in this course will be expected to do a considerable amount of independent study. Students enrolled in this course will participate in the American Computer Science League Contests. May be taken as either a one-semester (fall only), or yearlong course.