# 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 twenty-first 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 Science Department at Middlesex promotes in our students an understanding of the natural world and develops in them the ability to engage in scientific inquiry. We 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. Our students, after studying science at Middlesex, are informed citizens, adept problem solvers, effective collaborators, and savvy users of scientific data.

In the classroom, science at Middlesex emphasizes not only subject-specific knowledge but also critical thinking, problem solving, and effective communication of scientific ideas. Hands-on activities and laboratory experiments illustrate both the concepts and process of science. Students use technology to see principles of science in action and to learn to make conclusions about the world based on evidence. We expect students to be prepared for and engaged in the classroom, and teachers work with students to develop their skills and individual interests.

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 believe that most students at Middlesex should complete introductory courses in all three of the major disciplines of science: biology, chemistry, and physics. In most cases, students begin their lab science courses with biology, then chemistry, then physics. This is so that, as the students grow in mathematical maturity, they encounter greater quantitative challenges in their science courses. After they complete their introduction, we invite students to choose an area of interest for further exploration in our advanced courses, which include both AP and applied science courses.

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 applied science courses confer distributional credit, but do not confer credit for laboratory science.

##### Biology Courses: 2023-2024

**BIOLOGY 10 – Biology
**

*Fall. Open to all classes*.

*Biology 10 and Biology 11/12 constitute a full year course.*

This introductory course attempts to develop a basic understanding of how living organisms function. The course seeks to instill in the student a perspective of themselves as a living organism and to develop skills in experimental technique and scientific reasoning. Topics studied include anatomy and physiology, biochemistry, cellular biology, and energy processing. Students continue on to Biology 11 or Biology 12 in the spring semester.

**BIOLOGY 11 – Biology
**

*Spring. Open to all classes*.

*Prerequisite: Biology 10.*

This course is a continuation of Biology 10, with an emphasis on the concepts of cellular reproduction, genetics, evolutionary theory, and ecology.

**BIOLOGY 12 – Honors Biology
**

*Spring. 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 cellular reproduction, genetics, biotechnology, evolution, and ecology.

**BIOLOGY 20 – Advanced Placement Biology
**

*Year. Prerequisite: Biology, Chemistry 11 or higher, 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, biotechnology, 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 online resources to further explore the topics. This course prepares students for the Advanced Placement Examination in Biology.

##### Chemistry Courses: 2023-2024

**CHEMISTRY 09 – Chemistry
**

*Year. Open to all classes. Prerequisite: Completed or concurrent enrollment in Math 21.*

This year-long course is designed to develop fundamental study skills along with quantitative and conceptual understanding of chemistry. The general approach is based on the principle of modeling in which students generate physical, conceptual, and mathematical representations of real phenomena. Students are tasked with articulating and defending their ideas through the use of data and observations. Students will be introduced to concepts fundamental to studying matter at the molecular level. Learning will be done through discovery-based processes, work in small groups, and laboratory experimentation that involves qualitative analysis and quantitative techniques. Topics will include scientific measurement, atomic structure, periodic trends, chemical bonding, chemical reactions, stoichiometry, gas laws, electrochemistry, and acid-base chemistry. If time allows, advanced topics such as chemical kinetics, equilibrium, food chemistry or forensics may be explored. *Students who enroll in Chemistry 09 may not take Chemistry 10 or higher.*

**CHEMISTRY 10 – Accelerated Chemistry
**

*Fall. Open to all classes. Chemistry 10 and Chemistry 11/12 constitute a full year course. Prerequisite: Completed or concurrent enrollment in Math 31 in the spring semester.*

This course explores a core of principles that organizes the whole of chemistry. Coverage will include topics such as atoms and molecules, introduction to stoichiometry, 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. *Students may not take Chemistry 10 concurrent with or subsequent to Chemistry 09*.

**CHEMISTRY 11 – Accelerated Chemistry
**

*Spring. 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 on both the macroscopic, what is observable, and microscopic, particle level, 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 Accelerated Chemistry
**

*Spring. 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 takes on a more quantitative and data driven approach and is designed to reinforce and expand a student’s understanding of the topics covered.

**CHEMISTRY 20 – Advanced Placement Chemistry
**

*Year. Prerequisite: Chemistry 11 or higher, Physics, Math 39, 49 or higher 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 39 or 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 including atomic structure, compound structure and properties, intermolecular forces, chemical reactions, chemical equilibria, kinetics, thermodynamics, electrochemistry, spectroscopy, and acid-base 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: 2023-2024

**PHYSICS 10 – Physics
**

*Fall. Open to Classes I, II, and III. Prerequisite: completion or concurrent enrollment in Math 31. Physics 10 and Physics 11/12 constitute a full year course.*

*ExPRT Certificate eligible.*This course introduces the fundamental ideas of physics, emphasizing conceptual explanations and 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. Students will learn skills of data analysis, lab report writing, and design.

**PHYSICS 11 – Physics
**

*Spring.*

*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 circuits, magnetism, motion, free fall, forces, vectors, projectiles, and energy. Problem solving and conceptual explanations continue to be emphasized.

**PHYSICS 12 – Honors Physics
**

*Spring. 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 the completion of topics of circuits and electricity begun in Physics 10. It then turns to a description of motion (kinematics and vectors). Using these tools, the concepts of forces and conservation laws are applied to real world problems.

**PHYSICS 20 – Advanced Placement Physics 1: Algebra-Based
**

*Year. 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, power, and simple harmonic motion. 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. Open to Classes I and II. Prerequisite: Biology, Chemistry or higher, Physics 12 or higher 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 chemistry and physics.*

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 modern 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. 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: 2023-2024

**ENVIRONMENTAL SCIENCE 20 – Advanced Placement Environmental Science
**

*Year. Prerequisite: Biology, Chemistry 11 or higher or Chemistry 09 and Physics, and Permission of the Department. Preference will be given to members of Class I and II and students who have completed physics. In the case of over enrollment students will be ranked and admitted to the course based on their performance in previous science courses (biology, chemistry).*

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. 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.

##### Science Courses: 2023-2024

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

**SCIENCE 40 – Applied Science: Human Anatomy and Physiology
**

*Fall. Preference given to Class I and II.*

The structure and function of the human body have been a study for ages. This course offers a deeper examination of anatomical features and their function by examining individual body systems and connecting them into the larger context of function with the human body. With this, students will better understand concepts of homeostasis and how each system affects the next. While some may consider the study of anatomy and physiology a thing of the past, the implications of understanding these components are invaluable in health science. This course will be a mixture of lecture, lab, and discussion. Dissections will play an integral part in this course study. Students will be assessed both by tests and practicals related to the foundations of human anatomy.

**SCIENCE 41 – Applied Science: Marine Biology and Conservation Policy
**

*Fall. Preference given to Class I and II.*

Was the fishing out of Boston any better fifty years ago than today? Can humans still save the Great Barrier Reef? Why are there now hundreds of great white sharks in the waters off of Cape Cod? And why are some individuals opposed to conservation? This course seeks to answer these questions and many more. Primarily through the use of case studies, students will learn fundamental biological concepts related to topics of population growth, edge-effects, and predator-prey relationships, as well as the various ways humans have chosen to deal with marine ecosystems over the years. Topics will include local headlines, such as the relationship between growing seal and shark populations, while also incorporating broader global issues, such as overfishing and ocean pollution. Students will learn not only about marine biology, but also about stakeholders, regulators, and the political implications of conservation goals. The final research project will ask students to create a conservation plan for a marine species or region. By linking biological knowledge with political considerations, students will explore the complex and challenging world of marine biology and conservation policy.

**SCIENCE 42 – Applied Science: CSI: Middlesex – An Introduction to Forensic Science
**

*Spring. Preference given to Class I and II.*

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 44 – Applied Science: Biotechnology and Equity
**

*Spring. Preference given to Class I and II.*

This course examines the myriad of technological advances that have enhanced the study of the life sciences. Biotechnology is a study of life science through technical applications. These new and evolving technologies have furthered our own understanding of many molecular and cellular processes that can be harnessed for the benefit, and sometimes detriment, of society. This course will examine the intersections between these technologies and how they are often exploited to perpetuate systemic oppression and increase health disparities among marginalized communities. In this course, students will examine the most common tools utilized by researchers from the academic, medical, agricultural, industrial, and environmental fields, including gene manipulation, production of biological molecules, and gene mapping. Students will understand these techniques through a combination of laboratory experimentation, lectures, discussions, and dialogue about the context of these topics in current events. In this course, students will be evaluated by classroom participation, lab reports, and unit assessments.

**SCIENCE 45 – Applied Science: Advanced Astronomy
**

*Spring. Includes 1 evening observation session weekly. Prerequisite: Chemistry 09 or higher. 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 projects 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
**

*Fall. 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 48 – Applied Science: Engineering
**

*Fall. Preference given to Class I and II.*

**ExPRT Certificate eligible.**This 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. Preference given*

*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 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.

#### The Mathematics Department

The Mathematics Department aspires to lead students to greater understanding of and appreciation for the power of mathematics. Through courses ranging from the traditional algebra -geometry- calculus to our advanced topics offerings, students are encouraged to think in a quantitative fashion in order to model aspects of their experience and the world around them. Students should learn how to approach problems by integrating mathematical modeling, creative thought, and previous experience to find their way to a solution. To this end we support when needed, challenge when appropriate, inculcate sound reasoning skills, and encourage articulate communication of mathematical ideas. 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 when advantageous, and to welcome new challenges whose outcomes are unknown. Beyond this, we very much wish to impart a sense of the utility, power, and beauty 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.

Advancement in math courses is based on mastery of the material in a course. Any student who earns a grade below 70 or a semester grade between 70 and 75 and a cumulative exam score 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 75 regardless of the score on the cumulative exam for that course. Should a student taking a repeat course fail to make satisfactory progress in the repeat course, the student will be recommended to take a summer school course.

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. Math 37, 38 and the 40 – level courses may be taken in any order after completion of Math 32. In some instances, a student may wish to enroll in one of these courses concurrently with a core course Math 32 or below. This is allowed only with permission of the department. Students should note that Math 39 serves as the prerequisite for Advanced Placement courses in either statistics or economics and that Math 49 serves as a prerequisite for Advanced Placement courses in statistics, calculus, or economics.

##### Math Courses: 2023-2024

**MATH 12 – Intermediate Algebra
**

*Fall.*

This one-semester 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.*

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. 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. *New students who have not yet studied geometry will be placed into geometry in the SPRING semester.*

**MATH 31 – Advanced Algebra
**

*Fall, Spring.*

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 functions.

**MATH 32 – Pre-calculus: Trigonometry
**

*Fall, Spring.*

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 or concurrently with a math core course with the permission of the department.**

**MATH 37 – The Development of Mathematical Knowledge – Ancient Foundations
**

*Fall.*

Mathematical ideas have been developed independently by cultures across the globe. This course will introduce students to fields and applications of mathematics from a variety of ancient cultures in Africa, Asia, and the Americas expanding beyond a traditional Euro-centric focus. In addition to exploring and applying these ideas, incorporating problem-solving, reading, and writing, students will also learn and discuss the cultural and historical context leading to these developments.

**MATH 38 – The Development of Mathematical Knowledge – Asia and the Arab World
**

*Spring.*

This course will introduce students to mathematical developments from a variety of cultures in Asia and the Arab world. Students will explore ideas that have been built upon or borrowed as part of what we consider contemporary mathematics, even while they are not often credited in traditional Euro-centric textbooks. Through discussion of mathematics within a cultural context, students will develop insight into the modern concept of mathematics as it fits within their own cultures and communities.

**MATH 39 – Advanced Topics in Mathematics – Pre-calculus with Data Analysis
**

*Fall, Spring.*

This one-semester course continues the study of functions, introducing polynomial and rational functions. The concept of limits is introduced. Other topics will include sequences and series and applications. Students will gain skill in analyzing functions and making connections between analytic, graphical, and numeric representations. Students completing this course will be prepared to take calculus, though not at the AP level. *Students may not take Math 39 concurrent with or subsequent to Math 49.**This course satisfies the prerequisite for AP Statistics and AP Economics courses.*

**MATH 40 – Advanced Topics in Mathematics – Discrete Mathematics
**

*Fall, Spring.*

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 mathematics of finance.

**MATH 41 – Advanced Topics in Mathematics – Mathematical Modeling
**

*Fall.*

*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
**

*Spring.*

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. *As this is an introductory course, students who have taken Computer Science 21 or Computer Programming 26 or higher may not enroll in Math 42.*

**MATH 43 – Advanced Topics in Mathematics – Quantitative Analysis
**

*Fall.*

The focus of this course is on quantitative literacy — the ability to interpret, analyze, and interact with quantitative data and concepts, with an emphasis on financial markets. The course explores a variety of personal finance issues, including interest rates, comparing loan offers, taxes, retirement savings, and offers an introduction to statistics, probability, and game theory. The goal of this course is to explore the real-world application of mathematics in our everyday lives, emphasizing learning-by-doing using Excel and other online tools.

**MATH 44 – Advanced Topics in Mathematics – Problem Solving
**

*Spring.*

**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 – Seminar in Advanced Math Topics
**

*Fall.*

This course exposes students to some topics that are not covered in depth in our core curriculum. The specific topics covered will vary based on the interests of the students and the teacher but might include polar curves, parametric equations, imaginary numbers, conic sections, and 3D geometry. Students will investigate topics from both analytical and graphical perspectives as they collaboratively explore each topic. Students will use Desmos and other online tools to aid and enhance these explorations. Assessments may include written quizzes and tests as well as group project work. THIS COURSE WILL NOT BE OFFERED IN 2023-2024.

**MATH 46 – Advanced Topics in Mathematics – Calculus
**

*Spring. Preference given to Class I.*

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. Students will investigate limits and derivatives as tools for analyzing algebraic functions. Applications will include descriptions of motion, marginal analysis, and optimization. *This is an introductory course that cannot be taken concurrent with or subsequent to Math 50, 52, or 55. *

**MATH 47 – Advanced Topics in Mathematics – Statistics
**

*Fall, Spring. Preference given to Class I.*

This course covers many of the major topics of descriptive statistics. Topics covered will include displays of sample data, measures of center and spread, probability, discrete random variables, and normal distributions. *This is an introductory course that cannot be taken concurrent with or subsequent to Math 51. *

**MATH 48 – Advanced Topics in Mathematics – Inferential Statistics
**

*Spring. Prerequisite: Math 47.*

*ExPRT Certificate eligible.*This course builds upon topics covered in Math 47 with an increased focus on inferential statistics. Students will learn to test hypothetical claims, as well as look at different measures of location and variability. Students will examine fascinating questions about life and the world around them by investigating the underlying statistical questions which they can analyze through data and simulations in order to draw conclusions.* Students who enroll in Math 48 may not take Math 51.*

**MATH 49 – Advanced Topics in Mathematics – Pre-calculus
**

*Fall, Spring.*

This one-semester course is designed to prepare students who have shown significant interest in algebra for AP-level calculus. The focus of the course will be on problem solving using mathematical models to represent real world situations. Extensive detail is paid to polynomial and rational functions. Students will investigate sequences, series, and limits. *Students may not take Math 49 concurrent with Math 39**. This course satisfies the prerequisite for all AP level math and economics courses.*

**MATH 50 – Differential Calculus
**

*Spring. Prerequisite: Math 49 and Permission of the Department.*

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. Prerequisite: Math 39 or Math 49 and Permission of the Department.*

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. *Students may not take Math 51 after taking Math 48**.*

**MATH 52 – Advanced Placement Calculus AB
**

*Year. Prerequisite: Math 49 and Permission of the Department.*

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. *Students may not take Math 55 after taking Math 52**.*

**MATH 55 – Advanced Placement Calculus BC
**

*Year. Prerequisite: Math 50 and Permission of the Department.*

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. *Students may not take Math 55 after taking Math 52**.*

**MATH 60 – Multivariable Calculus
**

*Fall. Prerequisite: Successful completion of Math 55.*

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 2023-2024.

**MATH 61 – Introduction to Linear Algebra, Part I
**

*Fall. Prerequisite: Successful completion of Math 55*.

This is a course in the study of vector spaces and the structure of linear mappings between them. Topics in this course include vector spaces, matrices, linear transformations, and solutions of systems of linear equations.

**MATH 62 – Linear Algebra, Part II
**

*Spring. Prerequisite: Math 61.*

In this continuation of the study begun in Math 61, we will study eigenvalues, eigenvectors, and the diagonalization of matrices, along with applications to differential equations.

**MATH 65 – Vector Calculus
**

*Spring. 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 2023-2024.

#### The Computer Science Department

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 multiple 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 specific course sequence is designed for students desiring a general understanding of their technological world and the fundamentals of programming. Students in Computer Science 21 will also take the Advanced Placement Examination in Computer Science Principles.

Students seeking to develop extensive computer programming skills and pursue college-level coursework, should begin their computer programming study with Computer Programming 30, which in conjunction with Computer Programming 55 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, accomplished students can further their study through the Computer Programming 61-62 (algorithms and data structures) and Computer Programming 63-64 (data mining and analytics) course sequences, which are offered in alternating years. Students having completed these courses should possess the ability to use functional and object-oriented programming algorithms, constructs, data structures, and databases 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. 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.

Upon completion of any computer science course, students may additionally take a variety of topics courses (Computer Science 22, 24; Computer Programming 26, 28), which are offered on a rotating basis.

*The Computer Science 20-21 sequence is intended for students interested in learning more about exciting new ideas in computer science and developing fundamental programming skills.*

##### Computer Science Courses: 2023-2024

**COMPUTER SCIENCE 20 – Principles of Computer Science
**

*Fall. Prerequisites: Math 22, or Math 21 with 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 complex digital information such as numbers, text, images, and sound are represented and stored and how the logic behind these representations preserves essential qualities of the data. Fundamental programming concepts and collaborative software development processes will be studied enabling students to develop a variety of apps utilizing variables, conditionals, and functions. This course emphasizes creative problem solving and real-world applications that connect the material being studied to students’ everyday lives.

**COMPUTER SCIENCE 21 – Advanced Placement Computer Science Principles
**

*Spring. Prerequisite: Computer Science 20 and Permission of the Department.*

In this course, students will build upon the concepts studied in Computer Science 20 to create a wider variety of apps for the purposes of entertainment and solving problems. Students will design and analyze algorithms used for everyday computer tasks, explore logic behind data formatting, as well as research and debate current events at the intersection of internet, data, public policy, law, ethics, and societal impact. This course prepares students for the Advanced Placement Examination in Computer Science Principles, which involves the completion of a digital artifact that will be submitted to the College Board in addition to the student sitting for the Advanced Placement multiple-choice exam.

*The following Computer Science and Computer Programming topics courses are intended for eligible interested students. These courses are offered on a rotating basis.*

**COMPUTER SCIENCE 22 – Cyberethics
**

*Fall.*

This course considers both the legal and philosophical perspectives of the internet’s influence on our society and our lives. Students will gain a deeper understanding of current policies and issues surrounding censorship, intellectual property, information privacy, and cybersecurity. Case studies will include major corporate data breaches, fair use and the Crypto Wars, and the political impact of regulation and “fake news”. Students will be expected to contribute to class discussions daily, as well as write position papers throughout the semester.

**COMPUTER SCIENCE 24 – Website Development Tools
**

*Spring. Prerequisite: Completion of any Middlesex Computer Science or Computer Programming course, or its equivalent.*

**ExPRT Certificate eligible.**Websites are integral to the twenty-first-century workplace. Small local businesses, large corporations, academic institutions, and both local and national governments are just a few examples of entities that have recognized the importance of providing and maintaining a useful website. This project-focused course will teach students to design, build, and enhance their own personal website using HTML and CSS. Opportunities for developing additional enhancements using professional web development and graphic design software, PHP, and JavaScript will also be provided.

**COMPUTER PROGRAMMING 26 – Mobile App Development
**

*Spring. Prerequisite: Completion of any Middlesex Computer Science or Computer Programming course, or its equivalent.*

**ExPRT Certificate eligible.**This project-based course is designed to introduce students to the fundamental tools and algorithms necessary for development of mobile applications for both the Android and iOS platforms. Software such as Android Studio and XCode will be utilized to apply concepts such as touches, swipes, graphics, sounds, and game programming. Specialized topics such as maps, voice recognition, data retrieval, GPS, and encryption will also be incorporated. THIS COURSE WILL NOT BE OFFERED IN 2023-2024.

**COMPUTER PROGRAMMING 28 – Programming in Python
**

*Fall.*

**ExPRT Certificate eligible.**Python provides students with a solid platform of key problem-solving skills that translate easily across programming languages. This course incorporates comprehensive real-world projects in areas such as image processing, cryptography, astronomy, the Internet, and bioinformatics, to teach core design techniques and Python programming. Problem-solving, extrapolation, and the development of independent exploration and solution-building will be emphasized. While students solve problems of general interest, language elements are introduced with deliberate and incremental exposure to the fundamentals. THIS COURSE WILL NOT BE OFFERED IN 2023-2024.

*The following Computer Programming courses are intended for students interested in developing extensive programming skills.*

**COMPUTER PROGRAMMING 30 – Programming in Java
**

*Fall. 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.*

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. Prerequisite: Computer Programming 30 and Permission of the Department. Students will be ranked and admitted based upon their performance in Computer Programming 30.*

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 61 – Discrete Mathematics and Data Structures
**

*Fall. 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. Prerequisite: Computer Programming 61 and Permission of the Department.*

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 63 – Data Mining and Analytics
**

*Fall. Prerequisites: Computer Programming 55 and Permission of the Department.*

The volume of data around us is growing exponentially, and therefore possessing the skills to store, analyze, translate, and visualize that data become increasingly crucial in any field from civil engineering to risk management. This course introduces students to foundational methods to determine the effect of a variable on a population, linear regression, classification algorithms of two-dimensional data (a single independent variable used to estimate a dependent variable), strengths and weaknesses of these algorithms, and the respective implementations in the Python programming language. Moreover, students will hone their coding craft using industry tools to create meaningful scientific writing that seeks to answer questions about real world phenomena. THIS COURSE WILL NOT BE OFFERED IN 2023-2024.

**COMPUTER PROGRAMMING 64 – Advanced Data Mining and Analytics
**

*Spring. Prerequisites: Computer Programming 63.*

Building upon the work in Computer Programming 63, students in this project-focused course will be introduced to a library of different algorithms used to estimate and classify two-dimensional data. Techniques to rank algorithm performance in an unbiased way will be practiced and put to use in constructing analyses on datasets students select and process themselves. Students will need to show via writing and demonstration which method of estimation is most effective in terms of cost, accuracy, and versatility. Furthermore, students will learn to apply these skills and techniques using data in 3+ dimensions (using many independent variables in concert to estimate the dependent variable) and the challenges of these algorithms as well. THIS COURSE WILL NOT BE OFFERED IN 2023-2024.