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10 Hardest Classes at Carnegie Mellon

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Chelsea Wang

Many college students find that even though their university may provide a wide selection of courses outside their major that they can easily get high grades in, it is still important to take courses that are challenging and will exercise your brain. However, it is still important to realize that grades are not the most essential part about college, as long as you are learning enough to support your career path. Below are 10 of the hardest courses at Carnegie Mellon University, especially for freshmen and sophomores.

1. 15-251 – Great Ideas in Theoretical CS

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This course is about the rigorous study of computation, which can be described as the process of manipulating information. Computation is a fundamental component of minds, civilizations, nature and the universe. Therefore, having the right language and tools to reason about computation is an important goal. Students often find this course difficult because it teaches the mathematical underpinnings of computation and explores some of the central results and questions regarding the nature of computation, which may be something they have never seen before.

2. 15-213 – Introduction to Computer Systems

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This course provides a programmer's view of how computer systems execute programs, store information, and communicate. It enables students to become more effective programmers, especially in dealing with issues of performance, portability and robustness. It also serves as a foundation for courses on compilers, networks, operating systems, and computer architecture, where a deeper understanding of systems-level issues is required. Without a decent study group, this course can be especially challenging.

3. 15-410 – Operating System Design and Implementation

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This course is a rigorous hands-on introduction to the principles and practice of operating systems. The core experience is writing a small Unix-inspired OS kernel, in C with some x86 assembly language, which runs on a PC hardware simulator (and on actual PC hardware if you wish). Students find this course difficult because they often struggle with the core concepts such as the process model, virtual memory, threads, synchronization, and deadlock; the course also surveys higher-level OS topics including file systems, interprocess communication, networking, and security.

4. 10-315 – Introduction to Machine Learning

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This course covers the theory and practical algorithms for machine learning from a variety of perspectives. The course covers topics such as decision tree learning, Support Vector Machines, neural networks, boosting, statistical learning methods, unsupervised learning, active learning, and reinforcement learning, which are often quite difficult for students who have never worked with machine learning or artificial intelligence before.

5. 21-228 – Discrete Mathematics

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This course provides a general introduction to discrete mathematics. Students learn both classical methods for clever counting, as well as how to apply more modern methods to analyze recursions and sequences. Students also learn fundamental techniques in graph theory. Throughout the course, students encounter novel challenges that blur the lines between combinatorics and other subjects, such as number theory, probability, and geometry, so that they develop the skills to creatively combine seeming disparate areas of mathematics, which may also be the reason the course is so challenging.

6. 33-225 – Quantum Physics and Structure of Matter

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This course introduces the basic theory used to describe the microscopic world of electrons, atoms, and photons. The duality between wave-like and particle-like phenomena is introduced along with the deBroglie relations which link them. Students often find difficulty in developing a wave description appropriate for quanta which are partially localized and discussing the interpretation of these wavefunctions.

7. 21-420 – Continuous-Time Finance

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This course begins with Brownian motion, stochastic integration, and Ito's formula from stochastic calculus, some of the hardest courses in computational finance. This theory is used to develop the Black-Scholes option pricing formula and the Black-Scholes partial differential equation. Additional topics include models of credit risk, simulation, and expected utility maximization.

8. 36-402 – Undergraduate Advanced Data Analysis

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The goal of this class is to train students in using statistical models to analyze data — as data summaries, as predictive instruments, and as tools for scientific inference. The course builds on the theory and applications of the linear model, extending it to more general functional forms, and more general kinds of data, emphasizing the computation-intensive methods introduced since the 1980s.

9. 18-349 – Introduction to Embedded Real-Time Systems

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This practical, hands-on course introduces the various building blocks and underlying scientific and engineering principles behind embedded real-time systems. The course covers the integrated hardware and software aspects of embedded processor architectures, along with advanced topics such as real-time, resource/device and memory management. Students find difficulty in learning how to program with the embedded architecture that is ubiquitous in cell-phones, portable gaming devices, robots, tablets, etc.

10. 21-355 – Principles of Real Analysis I

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This course provides a rigorous and proof-based treatment of functions of one real variable. Students, especially non-math majors, often struggle with the topics which include the real number system: field and order axioms, suprema and infima, completeness, integers and rational numbers; real sequences: limits, cluster points, limsup and liminf, subsequences, monotonic sequences, Cauchy’s criterion, Bolzano-Weierstrass Theorem; etc.

These courses are perfect to take if you are willing to challenge yourself and don’t care too much about the grades. After all, college is about challenging yourself and learning new things while gaining independence and having the best experience.

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