### Natural Science

**PHY 101, Mechanics and Thermodynamics. (3). Credit 3 **

Mechanics and Thermodynamics Topics include: Units and physical quantities, vectors, motion in 1-dimension, motion in more than 1-dimension, Newton’s laws of motion and their applications, work and energy, potential energy and conservation law of energy, momentum and impulse, rotation of rigid bodies, dynamics of rigid bodies, gravitation, thermal properties of matter, laws of thermodynamics.

**Fulfils**: Natural Science Requirement – Mandatory for EE

**Prerequisite: **None

**PHY 101L, Mechanics and Thermodynamics Lab. (3). Credit 1**

Experiments include: simple harmonic motion observed through webcam, waves and oscillations, standing waves, resonance, moment of inertia of a tennis ball, rotational mechanics, rotational inertia, rotational friction, conservation of energy, latent heat of liquid nitrogen, heat capacity of solids, determined from boil-off of liquid nitrogen, conservation of momentum – elastic and inelastic collision, rotational motion, mass on a spring, basics of uncertainty analysis, Maxwell’s wheel, light polarization, heat transfer, conduction, convection, Newton’s law of cooling, temperature oscillations, Fourier analysis.

**Fulfils**: Natural Science Requirement – Mandatory for EE

**Prerequisite: **PHY 101

**PHY 102, Electricity and Magnetism. (3) Credit 3**

Electricity & Magnetism Topics include: Electromagnetism and electrostatics, electric charge, Coulomb’s law, electric field, Gauss’s law, electrostatic potential, magnetic fields, Biot-Savart law and Ampere’s law, magnetic materials, time-varying fields and Faraday’s law of induction, Hall effect, displacement current and Maxwell’s equations.

**Fulfils**: Physics Minor Foundational Course

**Prerequisite: **PHY 101

**PHY 102L, Advanced Physics Lab. (3) Credit 1**

Experiments include: determination of Curie point of a Ferro-magnet by controlled electric heating, observing Hall effect in semiconductors, magnetic moment of a conductor loop in a magnetic field, determining Verdet’s constant, Frank-Hertz Meter, determination of Planck’s constant from the spectrum of a tungsten light bulb, optical activity of a chiral (sugar) solution, imaging electron trajectories using a magic eye, image analysis, Lenz’s Law, band gap measurement of pure Ge, magnetic pendulum, exploring phase portraits, chaos, bifurcations, Spectral Lines of different gasses.

**Fulfils**: Physics Minor Foundational Course

**Prerequisite: **PHY 102

**PHY 104, Introductiont to Nano Science. (3). Credit 3**

Nano-Science is a significant area of Science which deals with the understanding of the properties of materials at nano-nanoscale—the world where atoms, molecules (atoms joined together), proteins, and cells rule the roost. It is the place where science and technology gain an entirely new meaning. This course offers a basic introduction to understand nanoscience and explore its applications through nanotechnology: where we can put the science into action to solve our problems.

**Fulfils**: Natural Science requirement and university wide free elective

**Prerequisite:** None

**PHY 201, Modern Physics. (3). Credit 3**

Topics include: Review of basic mechanics, introduction to special relativity, relativity and Physics, Planck’s radiation law, photo electric effect, Compton scattering, pair production, Bohr’s theory of Hydrogen atom, basics in quantum mechanics, Schrodinger’s equation and its applications, ideal gas equation, Maxwell’s distributions, Boltzmann’s distributions, Identical particles.

**Fulfils**: Physics Minor Foundational Course

**Prerequisite:** PHY 101, PHY 102, MATH 102, MATH 201/203

**PHY 202, Quantum Mechanics. (3). Credit 3 **

Topics include: Particle aspects of radiation, wave aspects of particles, quantum systems and indeterminacy, quantization rules, wave packets, mathematical tools of quantum mechanics, postulates of quantum mechanics, one-dimensional problems in quantum mechanics, angular momentum, more than 1-dimensional problems, rotations and addition of angular momenta, time dependent and independent approximation methods in quantum mechanics, scattering theory.

**Fulfils**: Physics Minor Foundational Course

**Prerequisite:** PHY 101, PHY 201, MATH 201/203

**PHY-300/CS-314, Quantum Computing. (3). Credit 3**

Quantum computers are physical devices that exploit the laws of quantum mechanics to solve certain problems faster than Turing machines, and in doing so negate the extended Church-Turing thesis, a fundamental conjecture in traditional computer science. Computer science students will learn a new and promising model of computation, and physics students will learn to analyze physical theories in terms of information and computation.

**Fulfils**: CS Theory Elective; Physics Minor

**Prerequisite: **Calculus 1, Calculus 2, Linear Algebra, Data Structures and Algorithm, OR Quantum Mechanics I OR instructor permission

**PHY 301, Classical Mechanics. (3). Credit 3**

Topics covered: Survey of elementary particles, variational principles and Lagrange’s equations, 94 central force problem, kinematics of rigid body motion, the rigid body equations of motion, oscillations, the Hamilton’s equations of motion, canonical transformations, and continuous classical systems.

**Fulfils**: Physics Minor Elective Requirement

**Prerequisite:** PHY 101, MATH 201/203

**PHY 302, Mathematical Methods for Physics. (3). Credit 3 **

Topics include: Tensors and their role in Physics, complex variable theory, linear integral equations, green’s functions, and introduction to group theory.

**Fulfils**: Physics or Math Minor Elective Requirement

**Prerequisite:** MATH 201/203

**PHY 351, Introduction to Statistical Mechanics. (3). Credit 3**

Statistical mechanics links the microscopic properties of physical systems to their macroscopic properties. Thermodynamics, which describes macroscopic properties, can then be derived from statistical mechanics with a few well motivated postulates. It leads to a microscopic interpretation of thermodynamic concepts, such as thermal equilibrium, temperature and entropy. In this course, the basic principles of statistical mechanics will be introduced with applications to the physics of matter.

**Fulfils**: This course is designed as an **independent study** to meet the elective requirement for a Physics minor.

**Prerequisite:** PHY 201 – Modern Physics, PHY 202 – Quantum Mechanics, PHY 301 – Classical Mechanics, MATH 202 – Engineering Mathematics, MATH 205 – Linear Algebra, ME 302 – Engineering Thermodynamics, EE 354 – Probability and Statistics

**PHY 352/MATH 352, Group Theory for Physicists. (3). Credit 3**

This course introduces students to group theoretic methods that allow them to analyze physical systems using symmetries. These methods are wide applicability in various branches of physics, as well as in Engineering and Computer Science. The identification of symmetries often lets one simplify a problem, and solve it in mathematically and conceptually elegant ways.

**Fulfils**: Physics minor, Mathematics Minor, Free Elective

**Prerequisite:** Calculus 1, Linear Algebra OR Instructor Permission

**PHY 401, Quantum Mechanics II, (3). Credit 3 **

Topics include: Recapitulation of classical field theory, path integrals in quantum mechanics, relativistic scattering theory, Quantum Mechanics and relativity, Klein Gordon equation, Dirac equation and representations of its solutions, (discrete) symmetries, and a basic understanding of interactions in quantum field theory.

**Fulfils**: Physics Minor Elective Requirement

**Prerequisite:** PHY 202, PHY 301, PHY 302

**ENER 104, Renewable Energy: Why, What and How?. (3+3), Credit 4**

Our reliance on energy systems has been increasing consistently since the industrial revolution. This reliance has increased greatly with the ongoing revolutions of infotech and biotech. While multiple alternate sources of energy are being used and researched, coal, oil and gas continue to be the world’s top energy sources accounting for about 65% of global demand. This over reliance on fossil fuels has resulted in an unprecedented emission of CO_{2} and other greenhouse gases which has triggered the first man made geological age which can threaten the existence of all living species on earth. It is not likely that we will reduce our energy needs anytime soon which makes it critical to find alternate energy sources that can fuel our energy needs while avoiding any negative impact on our environmental ecosystems. Through this course, we will explore why do we need renewable energy sources, what’s wrong with the current energy systems and what are the options available to us outside of regular sources of coal, oil and gas. We will study the operation of various renewable energy sources including, wind energy, solar energy, hydropower, biogas, hydrogen fuel cells and tidal energy. While using the current energy production and consumptions patterns, we will try to speculate the energy needs of Pakistan in the coming decades with a focus on energy needs by 2047. The course is supported through a lab where students will get to work with multiple renewable devices and analyze their functioning and limitations.

**Fulfils**: None

**Prerequisite: **This course meets Natural Science requirements for DSSE students and can count as a free elective to students from all other majors.

**BIO 101+BIO 101 L, Cell Biology & Public Health. (3+3). Credit 4**

This course provides an introduction to cellular and molecular biology and builds its connection with human biological processes; there will be a prime focus on developing skills to communicate biological concepts to laymen. Topics include: Prokaryotic and eukaryotic cells, structure and function of cellular organelles, cells tissues and organ systems, movement across cell membranes, cellular reproduction, DNA replication, transcription and translation, Mendelian genetics, blood groups, introduction to the immune system and vaccines, dengue viral infection, and cancer development. Workshops on communication design in public health will be integrated

**Fulfils**: Natural Science Requirement

**Prerequisite: **None

**BIO 102+BIO 102 L, The Secret World of Microbes. (3+3). Credit 4**

This course explores the vast realm of tiny, clever little beings that are present everywhere but are easily ignored as they are not visible to the naked eye. Microbes are microscopic living organisms that were the first to colonize earth. They are present everywhere; in the soil, air, water, food, even on our bodies. In fact, you can find more microbes on your hand than there are people on the entire planet. Albeit tiny, their role is so much more important. Without them, we couldn’t digest our food, garbage wouldn’t decay, our ecosystems would collapse. Even NASA has a team researching on the microbial life that can survive in space. Understanding microbes is essential to understanding the past and the future of ourselves and our planet. The reason bacteria serve as a valuable model system is because: a) they are easy and relatively cheaper to maintain, b) they take just 20-30 minutes to divide so generations can be studied in a short amount of time and c) they possess simpler biological systems reflective of complex organisms.

The lab component of this course is meant to be easy and fun! Discover how many microbes reside on your cell phone, laptop, bean bags of student lounge, or in the cafeteria food! Test which hand sanitizer or detergent works best, or who provides the most hygienic ‘gola ganda’ (ice candy) in town!

**Fulfils**: Natural Science Requirement

**Prerequisites: **None

**ENVS 102, Introduction to Environmental Systems. (3). Credit 3**

Environmental change as a result of human activities has emerged as the most pressing global challenge of our times, one with profound ecological, social and political implications and dire consequences. Addressing this challenge requires a rigorous understanding how natural systems operate and how human societies interact with these natural systems.

This survey course is designed to introduce students to the various environmental systems that enable life on earth and their linkages with human society. It is intended to be useful for both a broad-based introductory class on environmental science and as a useful supplement to specialist courses which wish to review the environmental systems dimensions of their areas of study. By covering a wide range of topics, review questions, case studies, and links to further resources, students will become conversant in the language and concepts of sustainability, and will be equipped for further study in sustainable management, planning, policy, economics, climate, ecology, infrastructure, and more.

**Fulfils**: Natural Science Requirement

**Prerequisites: **None

**BIO 121, Introduction to Biochemistry. (3). Credit 3**

Biochemistry is the study of life. This fascinating natural science will provide insights into the chemical processes driving the biological systems. This course will immerse you in the sub-cellular world to understand the processes that are integral for life. You will develop an appreciation of the basic principles of biochemistry and workings of the biological networks. Since the field of biochemistry is continually evolving, through this course you will be introduced to the biochemistry underlying some concepts such as molecular biology, genetics, evolutionary biology, plant biology, human physiology and the current advancements in the field of medicine. You will develop problem solving, critical thinking and analytical skills. The class and lab sessions will embrace variable teaching and learning strategies for audio and visual learners, including but not limited to flip classes, discussions, think-pair-share, activities, and video sessions, etc. Lab will include a combination of wet lab and virtual lab where the topics would range from detection and analysis of macromolecules, to isolating DNA from cells, testing blood sugars, and optimizing enzyme catalyzed reactions etc.

**Fulfils: **Natural Science Elective

**Prerequisite: **None

**BIO 151, Learning BioScience through Movies.(3). Credit (3)**

Are you interested in movies? Bioscience? Or both? This course is for you. Join Pakistan’s pioneering course on learning bioscience through movies. This course intends to mitigate the dichotomy between science and the arts. The underlying theme of the course is to learn different aspects of biology through movies. The course will provide insights into myriad of biological processes governing our world. You will appreciate the power of movies in developing an understanding of various biological phenomena. The course will focus on the following major themes: 1) Infections, 2) Human/animal experimentation and ethics, and 3) Plant biology. Within these themes, you will learn about the scientific method, evolution and survival of the fittest, ecological sustainability, genetic engineering, disease outbreaks, our body’s defense mechanisms, plant’s defense mechanisms, how plants communicate, strategies of risk assessment and risk communication, and much more. By analyzing movies, you will develop critical thinking and analytical skills. The class sessions will embrace variable teaching and learning strategies for audio and visual learners.

**Fulfils: **Natural Science Requirement

**Prerequisite: **Interest in movies and bioscience

**BIO/LIT 201, Digitally Yours Visual Novels About Diseases. (3). Credit (3)**

This interdisciplinary course explores digital narrative techniques focusing on key areas of disease/cell biology and empathy through storytelling. It examines the relationship between the afflicted and the caregivers, the reader and the sufferer through a mix of bioscientific knowledge and creative writing. The bio component of the course focuses on molecular and cellular functions during infectious and non-infectious diseases of contextual relevance. The course reconnoiters the rhetoric of empathy and the elucidations of science and art through the modern technology of Augmented Reality and Ren’Py (visual novels) and how that has changed our perceptions in a global, connected world.

**Fulfils**: Natural Science Requirement

**Prerequisite: **None

**BIO 211, Understanding the Human Body- The Physiology of Everyday Life. (3+3). Credit (4)**

In this course you will learn how we use our body every day to respond to an ever-changing environment, and the fascinating ways we deal with physical, emotional, and biological threats. You will understand how our heart and vessels work together to circulate the blood, all the amazing things our blood is capable of doing (from maintaining homeostasis to fighting infection), how our brain and nerves protect us, and how hormones ensure proper growth, development, and repair. You will explore our role in some of the common health problems afflicting mankind today, and develop a systematic, integrated understanding of how the body functions.

In the labs part, you will see these systems in action, and apply the concepts first hand by measuring blood pressure and heart rate, and relating it to exercise physiology. You will examine the blood composition and blood types, witness the microbes on and around you and test them against antibiotics, gather and interpret data on sleep quality, anxiety levels, eating behaviors, and traits such as focus, flexibility, and adaptability.

This course is for a diverse student pool and will be particularly interesting for individuals who are intrigued by the human body. There are no prerequisites and students with a non-biology background will equally enjoy the experience.

**Fulfils:** Natural Science Elective

**Prerequisite: **None

**ENVS 121, Water is Fighting over. (3). Credit (3)**

This course will expose students to important concepts in water resources policy and management. It is designed to help students majoring outside of science and engineering develop an informed perspective on 21^{st} century water challenges, and by extension, natural resource allocation problems. No pre-requisites are needed for this course.

**Fulfils:** Quantitative Reasoning and Natural Science requirement

**Prerequisite: **Basic Math

**ENVS 251 Water, Science, Society and Policy. (3). Credit (3)**

Should water be released from a reservoir to generate electricity or be stored and used later for agriculture? Should river flows be maintained to preserve ecosystems or does domestic water consumption take precedence? How do droughts and shortage of freshwater exacerbate tensions between countries sharing water resources?

Water serves a diverse set of societal needs (economic, ecologic, cultural etc.), and in an increasingly water-stressed world affected by climate change, these needs are often in conflict. In this three-part course, we will tackle the afore-mentioned questions. Students will first be introduced to hydrological processes in the environment (aka the ‘water cycle’). Next, we will focus on how various societies interact with the environment around them and in so doing, how they alter the hydrology around them. This will be done using case studies from around the world to investigate how changing hydrology due to climate change, and the various ways different societies use water, lead to conflicts. Finally, in the third part, students will learn about various stakeholder perspectives on Karachi’s water system. They will then use this information to present an equitable plan to better manage the City’s water system.

This course will expose students to important concepts in water resources policy and management. It is designed to help students develop an informed perspective on 21^{st} century water challenges, and by extension, natural resource allocation problems. No pre-requisites are needed for this course.

**Fulfils:** Natural Science Requirement

**Prerequisite: **None

**ENVS 301, Introduction to Environmental Engineering. (3). Credit (3)**

Environmental problems represent one of the gravest global challenges of the 21st century. Engineering sustainable solutions to these environmental issues is one of our most pressing needs. In this course, students will learn fundamental science and engineering principles needed for environmental engineering. Students will apply these principles to problems such as water supply and treatment systems, sewage treatment of municipal and industrial wastewaters, stream and air pollution, and disposal of solid waste materials. In addition, this course will provide an overview of major themes in contemporary environmental engineering, including environmental impacts of socioeconomic changes, energy consumption and production, water supply and treatment, air pollution and global climate change.

**Fulfils:** Natural Science Requirement

**Prerequisite: **Engineering Math

**BTEC 101, Introduction to Biotechnology. (3). Credit 3 **

This course provides an introduction to the fundamentals of biotechnology and its applications. Topics include: an overview of biotechnology and its current importance in society, rapid growth of biotechnology in agriculture, environment, industry, and medicines, antibiotics/antibodies biotech. Emphasis will be placed on DNA manipulation sciences including genetic engineering, gene cloning, plasmids as cloning vectors, restriction enzymes, DNA ligase, PCR, biotransformation, E. coli host as model system, mutagenesis, manipulation of expression of desired DNA, strategies of protein purification, stem cell biotech, and ethics of biotechnology.

**Fulfils:** Natural Science Requirement

**Prerequisite:** School / college level Biology or chemistry or permission of instructor

**BTEC 101L, Biotech Laboratory Practices. (3). Credit (3)**

This laboratory course provides practical insights into the role of DNA sciences in achieving and improving the technological applications to develop products to improve quality of life. Topics include: basic operations used in biotech labs, DNA extraction from living organisms, DNA cut and clone, making lots of copies of DNA, overproduction of protein, purification, plasmid isolation, DNA manipulation by PCR, transformation of E. coli with a recombinant plasmid, DNA purification and quantification, calorimetric detection of DNA, visualizing of DNA on gel electrophoresis and DNA fingerprinting.

**Fulfils:** Natural Science Requirement

**Corequisite:** BTEC 101

**BIO 111 + BIO 111L, Food and Nutrition. (3+3). Credit (4)**

The course covers a wide range of knowledge from the basics of nutritional science to the use of food for preservation and management of health. It provides an overview of the social and cultural shifts in food consumption that contributed to the modern epidemics of chronic conditions such as obesity, diabetes and cardiometabolic disorders.

The overarching aims of this elective course are following:

– Provides an introduction to food sciences and nutrition research

– Evoke global thinking and international mindedness

– Critique on how you know what you know

– Experience the scientific method in action: Observe/Explore, Re-search, Conclude, Repeat

– Instill life-long learning

**Fulfils:** Natural Science Requirement

**Prerequisite:** None

**BIO 103, Global Health and Disease. (3). Credit (3)**

The course covers a wide range of knowledge from the basics of global health and disease, to an overview of communicable and non-communicable diseases worldwide, to the role of life science technology and drug design in human development.

The overarching aims of this elective course are following:

– Provides an introduction to global health and disease

– Evoke international mindedness

– Infuse a holistic transdisciplinary approach to tackle global issues

– Instill life-long learning and critical-thinking and problem-solving skills

**Fulfils:** Natural Science Requirement.

**Prerequisite**: None

**SCI 101, Introduction to Sustainability. (3). Credit (3)**

This course is designed to introduce the essential concepts of sustainability. This subject is of vital importance as it seeks to uncover the principles of the long-term survival and welfare of all the inhabitants of our planet. The course is intended to be useful for both a broad-based introductory class on sustainability and as a useful supplement to specialist courses which wish to review the sustainability dimensions of their areas of study. By covering a wide range of topics, review questions, case studies, and links to further resources, students will become conversant in the language and concepts of sustainability, and will be equipped for further study in sustainable management, planning, policy, economics, climate, ecology, infrastructure, and more.

**Fulfills:** This course is part of the Habib Liberal Core and meets the requirements for Quantitative Reasoning and Natural Science courses.

**Prerequisite:** None

**BIO 102+BIO 104L, Introduction to Ecology and Evolutionary Biology. (3+3). Credit 4**

Understanding how nature functions is necessary in order to develop environmental protection, conservation and resource management policies that work. The goal of this course is to familiarize students to ecological and evolutionary concepts that govern natural systems, so that they are able to make informed decisions on pressing social issues in Pakistan, such as global climate change, conservation of biodiversity, human population growth and resource management. This course is divided into two sections: 1) Evolution and Adaptation, and 2) Ecology and Biodiversity. Each lecture (3 hours) will be accompanied by a laboratory session (3 hour) where students will discuss and explore the concepts learned during lecture.

**Fulfills:** It fulfills Natural Science requirement for SSE students.

**Prerequisites:** None

**BIO 114+BIO 114L, Biodiversity in the city. (3+3). Credit 4**

Habitat alteration as a result of human activity is one of the leading threats to global biodiversity. Urbanization as a process significantly alters temperature, noise, air quality, hydrology as well as many abiotic factors. In this course, we will explore and document the communities of organisms that exist in Karachi alongside humans. We will investigate the consequences of urban environments and human social behavior on ecological systems and discuss factors such as nutrient cycling, behavior, phenology, disease, and patterns and process of biodiversity in urban systems, and importance of ecosystem services provided by these communities. In addition, we will discuss best practices in urban planning and development for promoting and preserving biodiversity and ecosystem processes. A significant component of this course will involve discussion of current scientific literature. This course will have a lab component where students will perform biodiversity surveys of plants, arthropods, and birds in their mohallas, examine the impacts of different urban activities on ecological communities and develop plans for protecting and promoting biodiversity across Karachi.

**Fulfills:** It fulfills Natural Science requirement University’s Habib Liberal Core.

**Prerequisites:** None

**CORE 100, Climate Change and US. (3). Credit (3)**

We live in a world where climate change has become an inescapable reality. It’s like the dice has been rolled and we can now only wait and see what consequences it brings. Climate change is starting to influence all areas of our lives from food production, melting icecaps to frequent natural disasters. This course will develop a conceptual understanding of all the issues and impacts related to climate change and provide an opportunity to develop sustainable adaptation plans.

This course is designed to provide an introduction to climate change and its impacts on various aspects of our lives. The topic of climate change will be explored from different lenses such as its effects on humans, water, food, melting glaciers, and oceans among others. The course hopes to not only engage student learning through traditional teaching strategies but to bring in the expert knowledge that documentaries, case studies and guest speaker sessions offer us to fully cover every aspect of this global issue.

**Fulfills:** “This course falls under the Form of Thought of Quantitative Reasoning. It also fulfils Natural Science requirement for SSE students.”

**Prerequisites:** None

**SCI 122, Inventing the information Age. (3). Credit 3**

Our current era is often referred to as the information age, because of the widespread use of information processing capabilities that are used for human benefit in a wide variety of ways. This era is enabled by a number of scientific and technological inventions such as computers and communication technologies. The effect of these inventions has been felt through significant social, economic and political change.

This course surveys the key physics, mathematics and computer science inventions that enable the information age. We will study the basics of important physical constraints and phenomena that are used to build information processing devices. We will understand how coding theory allows us to reliably transmit, store and compute information on error prone physical devices. We will also discuss essential cryptographic techniques to securely transmit and store important information. The course will end with an outlook of future innovations that will further enhance humanities’ information processing capabilities.

**Fulfils: **Natural Science elective, CS elective

**Prerequisite: **None

**SCI 221, Design thinking for Sustainability. (3). Credit 3**

This course provides an introduction to the principles of design thinking and allows an opportunity to deploy these principles for solving a sustainability challenge. Design thinking offers a systematic approach to unleash the innovative and creative forces of individuals in a collaborative space. It applies methodologies of design to solve challenges to the environment and society and at the same time provides a more engaged and practical learning opportunity.

The course will involve a human-centered design process where the students will learn and work in a team-based community project throughout the semester. Their learning will be supported through readings, workshops, videos, discussions, in-class activities and reflection assignments. Students will also spend a significant amount of time observing, listening, analyzing, discussing, reflecting and engaging with their classmates as they design, develop and implement meaningful and innovative projects on sustainability

**Fulfills:** “This course falls under the Form of thought of Creative Practice”

**Prerequisites:** Introduction to Sustainability/Energy/Climate change & us.

### Mathematics

**MATH 012, Pre-Calculus. (3). Credit 3**

Topics include: A revision of the number systems and relations, functions, and polynomials with symbolic and graphic representations. These topics will cover a wide range of subtopics to bridge the gaps in high school mathematics, like rational functions, inverse functions, logarithmic and exponential Functions followed by trigonometric Functions with an extensive treatment in the course. As a learning outcome students are expected to be able to analyze functions and their behaviors symbolically, numerically and graphically.

**Prerequisite: ** High school mathematics of any level.

**MATH 101, Calculus I. (3). Credit 4 **

Topics include: An overview of functions and their behavior in terms of rates of change, average vs. instantaneous rates of change, the derivative and shortcuts to differentiation, optimization (finding relative extrema / critical points), related rates, area under a curve, Riemann sums and the definite integral, the general antiderivative, approximation of definite integrals, techniques of integration and improper integrals.

**Fulfils:** Mandatory Math requirement for all DSSE students

**Prerequisite: ** None

**MATH 102, Calculus II. (3). Credit 3**

Topics include: A look at finding volumes of revolution using a Riemann Sums approach to integration, an introduction to first order differential equations and slope fields, parametric equations and graphs and finding area and arc length of parametric curves, polar coordinates and polar functions with areas and arc length of polar curves, functions of severable variables, partial derivatives and the equation of a tangent plane to a surface, basic vector algebra with dot and cross product derivations, directional derivatives, optimization and the second derivative test for functions of two variables, optimization with Lagrange multipliers, integrating functions of several variables with double and triple integrals evaluated in Cartesian, cylindrical and spherical coordinates, parametrization of lines and curves in 3-space, vector fields, line integrals, and the fundamental theorem of calculus for line integrals.

**Fulfils:** Mandatory Math requirement for all DSSE students

**Prerequisite: ** MATH 101

**MATH 105, The Art of Mathematics. (3). Credit (3)**

This course will explore multiple theorems, arguments, and quantities that have been relevant to a variety of fields through history, such as art, architecture, astronomy, and the physical sciences. Tracing the birth of geometric reasoning from the time of Euclid to looking at the birth of trigonometry as a tool for astronomical calculations and models, students will be introduced to geometry, algebra, and topology through various contexts. Students will be expected to use these concepts to create culminating projects using design and mathematical software.

Note: This course will also fulfil one (01) of the math requirements for the students pursuing a Communication and Design major.

**Fulfils:** Elective for Math Minor and fulfils Quantitative Reasoning requirement for AHSS students

**Prerequisite: ** None

**MATH 106, Music and Mathematics. (3). Credit (3) **

This course will introduce the rudiments of Western and South Asian musical theory, with a focus on the mathematics incorporated in their development and overall structure. The course will explore the properties of the twelve-tone scale, the historical evolution of tuning and temperament, the idea of combinational tones and consonance, and the physics behind the construction of musical 96 instruments. Looking primarily at South Asian and Western musical genres, students will also analyze the mathematics involved in music composition, for both melody and rhythm.

**Fulfils:** Elective for Math Minor and fulfils Quantitative Reasoning requirement for AHSS students

**Prerequisite: ** None

**MATH 107, Lie Detector: An Introduction to the Practice of Statistics. (3). Credit (3)**

In the age of big data, it is difficult to differentiate knowledge from misinformation. Statistics, as a field, is concerned with quantifying uncertainty. Statistics are tools to summarize and describe patterns in reality and to explore the causal processes leading to these patterns. Understanding how statistics are used and misused is vital for assessing and assimilating information in any field. The goal of this course is to help students understand the philosophy of inference, develop a scientific process for posing questions, collecting and interpreting relevant data, and familiarize them with common statistical tools so that they can apply evidence based decision making in their lives. We will review core principle and concepts in probability and statistics, using project based learning to focus on practical application rather than theory. All students are expected to attend three hour computer labs every week where they will be using the R statistical language to review statistical concepts and principles learned during lecture. This course is aimed at all SSE and AHSS students, especially those who are intimidated by mathematics, working with numbers or programming.

**Fulfils:** It fulfills quantitative reasoning requirements for AHSS and SSE students

**Prerequisite: ** None

**MATH 202, Engineering Mathematics. (3). Credit (3)**

Topics include: Vector Calculus (vector functions, line and surface integrals). Elementary methods for solving first order ODEs (direct integration and substitution) with geometric interpretation and classification, separable ODEs, method of integrating factors. Vector algebra (including matrix algebra, eigenvalues and eigenvectors, quadric surfaces). Dynamical systems (linear systems of ODEs, stability and phase portraits of dynamical systems). Second, order ODEs – elementary methods including their classification, reduction of order techniques, linear second order ODEs with constant coefficients, and finding particular solutions. Orthogonal functions and Fourier series solutions (generalized and trigonometric methods), convergence in the mean and pointwise convergence, odd and even expansions, half-range expansions. Partial differential equations (PDEs) (wave, heat and Laplace equations), solutions using Fourier series and Laplace transforms, and Schr dinger equation.

**Fulfils:** Mandatory Math requirement for all DSSE students

**Prerequisite: ** MATH 102

**MATH 203, Advanced Differential Equations. (3). Credit (3) **

Topics include: A brief revision of first- and second-order ordinary differential equations (ODEs) with constant coefficients. Differential operators, Wronskian and linear independence. Numerical solution methods for ODEs: Euler method, Taylor series solution up to 2nd order, Runge-Kutta methods up to 2nd order; Cauchy-Euler equations; Power series and Frobenius’ methods including Ordinary points, singular points, regular points, analytic functions, indicial equation. Bessel function and Bessel’s equation, Legendre equations. Boundary value problems for homogeneous linear 2nd order ODEs: Boundary values, Sturm-Liouville problem, eigen functions and corresponding eigenvalues, Fourier Bessel series. Inner products and norms of functions. Self-adjoint operators, and Schro dinger equation.

**Fulfils:** Math Minor Elective

**Prerequisite: ** MATH 201 for CS and EE students. MATH 102 with min 70% score for non-engineering students in MATH Minor.

**MATH 205, Linear Algebra. (3). Credit (3) **

Topics covered: A brief revision of vector algebra including lines and planes in 3D and matrices, Determinants, Symmetric matrices, and quadratic forms; Elementary row and column operations of a matrix; Systems of linear equations and their solutions, existence, and uniqueness of solutions; Vector spaces; Inner products and ortho-normalization; Orthogonal transformations and rotations; Linear transformations, orthogonality, QR factorization, Hermitian and Unitary transformations; Least squares analysis and approximations; Singular value decomposition; Direct sum decomposition; and Caley-Hamilton Theorem.

**Fulfils:** Mandatory Math requirement for all DSSE students

**Prerequisite: ** MATH 201

**MATH 304, Real Analysis. (3). Credit (3)**

In this course, we try to understand and appreciate the rigor that mathematics is known for. For all its applications, we must be able to say with absolute certainty that, given a small set of axioms and the rules of logic, our mathematics is consistent.

The course is intended to expose the students to the basic ideas of Real Analysis. Some of the questions that we address are as follows:

-What are real numbers?

-Is there a largest real number?

-What is the real number that comes directly after 0?

-Are there any ‘holes’ in the real number line?

Even numbers and odd numbers add up to form natural numbers, does that mean even numbers are less than natural numbers? What about the size of real numbers compared to the size of natural numbers? Are there more than one infinities?

What are sets? Functions? Measure and distance? Continuity?

**Fulfils:** This course meets elective requirements for EE and CS programs as well as minor in Mathematics.

**Prerequisite: ** Math101, Math102

**MATH 305, Complex Analysis. (3). Credit (3)**

Specific topics covered in this course are: Complex Algebra and the Complex Plane and its Motivation, Polar Form, Complex Exponential, deMoivre’s Theorem, Powers and Roots, Sets of Points, Complex Functions and Linear Mappings ,Limits and Continuity for Real and Complex Functions, Differentiability and Analyticity, Cauchy-Riemann Equations, Harmonic Functions, Elementary functions (Exponential, Trigonometric and Logarithmic Functions and Complex Powers), Line & Contour Integrals, Complex Integration, Cauchy’s Integral Formulas, Sequences and Series , Taylor Series, Power Series, Convergence, Laurent Series, Zeros and Poles, Newton’s Method and Fractals, Residues and Residue Theorem

**Fulfils:** Math Minor Elective

**Prerequisite: ** Calculus 1 (Math 101) *, *Calculus 2 (Math 102)

**MATH 333, History of Number Theory. (3). Credit (3)**

Number Theory, or arithmetic/higher arithmetic, as it was called in ancient times, is one of the oldest and most popular branches in mathematics, as its problems are easy to comprehend, yet sometimes incredibly hard to solve. Brahmagupta concluded over 2500 years ago, when studying arithmetic, that “These problems arestated merely for pleasure. The wise man can devise a thousand rules or he can solve the problems of others by the rules given here. As the sun obscures the stars so does the man of knowledge eclipse the glory of other mathematicians in an assembly of people by proposing algebraic problems and still more by solving them.”

Positive integers are seen to be the first mathematical creation of humans and we are going to start the course by introducing different ancient number systems in various civilizations and the first arithmetic operations. After this introduction we are going to focus on mathematics in ancient Greece, mainly under Plato, Euclid and Diophantus and in particular the connection between geometry and number theory that they established (It will also be highlighted if similar discoveries were made for example in India).

The course will then continue with medieval Islamic mathematics, their appropriation of Greek, Indian and Persian texts resulting in the Hindu-Arabic number system and further studies on ‘special’ numbers, such as perfect numbers, primes, amicable numbers and their properties and the influence of al-Khwarizmi’s introduction of Algebra on number theory problems. This will then segue into Europe in the late Renaissance, thanks to a renewed study of the works of Greek antiquity (often arriving in Europe in Arabic). A catalyst for this was the textual emendation and translation into Latin of Diophantus’ Arithmetica leading to what is today called early modern number theory and names like Fermat, Euler, Legendre, Lagrange, Gauss, Dirichlet, Riemann…. Many of the most famous mathematicians of that time were actually (at least partially) studying number theory problems, as the German mathematician Carl Friedrich Gauss once said, “Mathematics is the queen of the sciences—and number theory is the queen of mathematics.” As today Number Theory tends to be split in algebraic and analytic number theory, the course will also introduce some helpful algebraic and analytic ideas giving an insight into those disciplines. In addition students will be expected to cover the history of cryptography from the Greeks to modern cryptography (using number theory) through project presentations, in order to get an idea of this famous application of number theory, in particular since the invention of computers.

**Fulfils:** Math Minor Elective

**Prerequisites****:** N/A

**MATH 351, Toplogy. (3). Credit (3)**

The independent study is designed to be a first introduction to Point-Set Topology. The last few weeks are dedicated to understanding the basics of another aspect of topology, namely Algebraic Topology.

The topics are particularly chosen in such a way as to equip the students to later diverge into different streams within topology according to their interests.

**Fulfils:** This course meets elective requirements for EE and CS programs as well as minor in Mathematics.

**Prerequisites****:** Math101, Math102

**EE 354/MATH 310, Introduction to Probability and Random Variables. (3). Credit (3)**

In the present world, we encounter situations where we have to make decisions on the basis of incomplete or imperfect information. The theory of probability helps provide a formal mechanism for understanding, quantifying, and dealing with uncertainty, which is ever present in our lives, pure science, or engineering applications. Simply, by uncertainty we mean the condition when outcomes or future are not completely determined or can be captured by a deterministic function; they depend on a number of factors and perhaps just on pure chance. A lot of our present day technologies will not be possible without an understanding of how to make decisions in presence of uncertainty. These technologies include all forms of wireless communication, servers, speech processing systems, network systems and so many more. Equipping yourself with tools to deal with uncertainty will help you with whatever you wish to pursue in life.

This course will cover the foundations of probability, random variables and statistics, with a plethora of examples from electrical engineering, computer engineering, computer science, and everyday life. The course content can broadly be divided into three categories:

- Fundamentals of probability,
- Common probability models,
- Inferences & statistics.

**Fulfils:** This course meets program requirements for EE & CS Majors & Quantitative Reasoning (QR) forms of thought for EE & CS Majors.

**Prerequisites:** Math 102, Basic knowledge of MATLAB or some other programming language, Rudimentary linear algebra