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MECH_ENG 513: Professional Essentials


Seminar course covering techniques for teaching and technical presentation skills, organizational issues associated with teaching and presentations. Active teaching duties will be assigned during the course and performance feedback provided.

Who Takes It

This is a seminar course taken by ME graduate students to improve their skills of teaching, seminar presentations, technical and proposal writing. The seminar course is required for all ME PhD students.

What It's About

This course meets once per week, and each session is run by different faculty members in an innovative forum to address the syllabus topics. The purpose is to expose students to a variety of skills necessary to advance as a researcher during and after their PhD studies.

The topics of teaching and technical writing and presentation are incredibly important in a student's future success and yet are seldom taught in a systematic fashion in standard PhD curricula. This course addresses this need by tackling these topics drawing on the expertise of our own faculty.

The course is about 1/2 seminar and 1/2 interactive discussion. Some sessions are run as panel discussions and in several areas students will actively participate and be provided feedback on their performance by the faculty. Areas for student activity include preparation and presentation of a short mini-lecture on a research topic, and writing a proposal for a research or teaching lab need.

Evaluation Method

No grade is given in this zero credit seminar class. Class attendance and participation is mandatory to meet the requirements for the PhD degree in Mechanical Engineering.

10 Day Trading Tips for Beginners

Day trading is the act of buying and selling a financial instrument within the same day or even multiple times over the course of a day. Taking advantage of small price moves can be a lucrative game if it is played correctly. Yet, it can be dangerous for beginners and anyone else who doesn't adhere to a well-thought-out strategy.

Not all brokers are suited for the high volume of trades day trading generates. On the other hand, some fit perfectly with day traders. Check out our list of the best brokers for day trading for those that accommodate individuals who would like to day trade.

The online brokers on our list, Interactive Brokers and Webull, have professional or advanced versions of their platforms that feature real-time streaming quotes, advanced charting tools, and the ability to enter and modify complex orders in quick succession.

Below, we'll take a look at ten day trading strategies for beginners. Then, we'll consider when to buy and sell, basic charts and patterns, and how to limit losses.

Key Takeaways
  • Day trading is only profitable in the long run when traders take it seriously and do their research.
  • Day traders must be diligent, focused, objective, and unemotional in their work.
  • Interactive Brokers and Webull are two recommended online brokers for day traders.
  • Day traders often look at liquidity, volatility, and volume when deciding what stocks to buy.
  • Some tools that day traders use to pinpoint buying points include candlestick chart patterns, trendlines and triangles, and volume.
  • 1. Knowledge Is Power

    In addition to knowledge of day trading procedures, day traders need to keep up with the latest stock market news and events that affect stocks. This can include the Federal Reserve System's interest rate plans, leading indicator announcements, and other economic, business, and financial news.

    So, do your homework. Make a wish list of stocks you'd like to trade. Keep yourself informed about the selected companies, their stocks, and general markets. Scan business news and bookmark reliable online news outlets.

    2. Set Aside Funds

    Assess and commit to the amount of capital you're willing to risk on each trade. Many successful day traders risk less than 1% to 2% of their accounts per trade. If you have a $40,000 trading account and are willing to risk 0.5% of your capital on each trade, your maximum loss per trade is $200 (0.5% x $40,000).

    Earmark a surplus amount of funds you can trade with and are prepared to lose.

    3. Set Aside Time

    Day trading requires your time and attention. In fact, you'll need to give up most of your day. Don’t consider it if you have limited time to spare.

    Day trading requires a trader to track the markets and spot opportunities that can arise at any time during trading hours. Being aware and moving quickly are key.

    4. Start Small

    As a beginner, focus on a maximum of one to two stocks during a session. Tracking and finding opportunities is easier with just a few stocks. Recently, it has become increasingly common to trade fractional shares. That lets you specify smaller dollar amounts that you wish to invest.

    This means that if Amazon shares are trading at $3,400, many brokers will now let you purchase a fractional share for an amount that can be as low as $25, or less than 1% of a full Amazon share.

    5. Avoid Penny Stocks

    You're probably looking for deals and low prices but stay away from penny stocks. These stocks are often illiquid and the chances of hitting the jackpot with them are often bleak.

    Many stocks trading under $5 a share become delisted from major stock exchanges and are only tradable over-the-counter (OTC). Unless you see a real opportunity and have done your research, steer clear of these.

    6. Time Those Trades

    Many orders placed by investors and traders begin to execute as soon as the markets open in the morning, which contributes to price volatility. A seasoned player may be able to recognize patterns at the open and time orders to make profits. For beginners, though, it may be better to read the market without making any moves for the first 15 to 20 minutes.

    The middle hours are usually less volatile. Then, the movement begins to pick up again toward the closing bell. Though rush hours offer opportunities, it’s safer for beginners to avoid them at first.

    7. Cut Losses With Limit Orders

    Decide what type of orders you'll use to enter and exit trades. Will you use market orders or limit orders? A market order is executed at the best price available at the time, with no price guarantee. It's useful when you just want in or out of the market and don't care about getting filled at a specific price.

    A limit order guarantees price but not the execution. Limit orders can help you trade with more precision and confidence because you set the price at which your order should be executed. A limit order can cut your loss on reversals. However, if the market doesn't reach your price, your order won't be filled and you'll maintain your position.

    More sophisticated and experienced day traders may employ the use of options strategies to hedge their positions as well.

    8. Be Realistic About Profits

    A strategy doesn't need to succeed all the time to be profitable. Many successful traders may only make profits on 50% to 60% of their trades. However, they make more on their winners than they lose on their losers. Make sure the financial risk on each trade is limited to a specific percentage of your account and that entry and exit methods are clearly defined.

    9. Stay Cool

    There are times when the stock market tests your nerves. As a day trader, you need to learn to keep greed, hope, and fear at bay. Decisions should be governed by logic and not emotion.

    10. Stick to the Plan

    Successful traders have to move fast, but they don't have to think fast. Why? Because they've developed a trading strategy in advance, along with the discipline to stick to it. It is important to follow your formula closely rather than try to chase profits. Don't let your emotions get the best of you and make you abandon your strategy. Bear in mind a mantra of day traders: plan your trade and trade your plan.

    Investopedia / Madelyn Goodnight

    What Makes Day Trading Difficult?

    Day trading takes a lot of practice and know-how and there are several factors that can make it challenging.

    First, know that you're going up against professionals whose careers revolve around trading. These people have access to the best technology and connections in the industry. That means they're set up to succeed in the end. If you jump on the bandwagon, it usually means more profits for them.

    Next, understand that Uncle Sam will want a cut of your profits, no matter how slim. Remember that you'll have to pay taxes on any short-term gains—investments that you hold for one year or less—at the marginal rate. An upside is that your losses will offset any gains.

    Also, as a beginning day trader, you may be prone to emotional and psychological biases that affect your trading—for instance, when your own capital is involved and you're losing money on a trade. Experienced, skilled professional traders with deep pockets are usually able to surmount these challenges.

    Day Traders Lose

    A study by the Securities and Exchange Commission revealed that traders usually lose 100% of their funds within a year.

    Deciding What and When to Buy What to Buy

    Day traders try to make money by exploiting minute price movements in individual assets (stocks, currencies, futures, and options). They usually leverage large amounts of capital to do so. In deciding what to buy—a stock, say—a typical day trader looks for three things:

  • Liquidity. A security that's liquid allows you to buy and sell it easily, and, hopefully, at a good price. Liquidity is an advantage with tight spreads, or the difference between the bid and ask price of a stock, and for low slippage, or the difference between the expected price of a trade and the actual price.
  • Volatility. This is a measure of the daily price range—the range in which a day trader operates. More volatility means greater potential for profit or loss.
  • Trading volume. This is a measure of the number of times a stock is bought and sold in a given time period. It's commonly known as the average daily trading volume. A high degree of volume indicates a lot of interest in a stock. An increase in a stock's volume is often a harbinger of a price jump, either up or down.
  • When to Buy

    Once you know the stocks (or other assets) you want to trade, you need to identify entry points for your trades. Tools that can help you do this include:

  • Real-time news services: News moves stocks, so it's important to subscribe to services that alert you when potentially market-moving news breaks.
  • ECN/Level 2 quotes: ECNs, or electronic communication networks, are computer-based systems that display the best available bid and ask quotes from multiple market participants and then automatically match and execute orders. Level 2 is a subscription-based service that provides real-time access to the Nasdaq order book. The Nasdaq order book has price quotes from market makers in every Nasdaq-listed and OTC Bulletin Board security. Together, they can give you a sense of orders executed in real time.
  • Intraday candlestick charts: Candlesticks provide a raw analysis of price action. More on these later.
  • Define and write down the specific conditions in which you'll enter a position. For instance, buy during uptrend isn't specific enough. Instead, try something more specific and testable: buy when the price breaks above the upper trendline of a triangle pattern, where the triangle is preceded by an uptrend (at least one higher swing high and higher swing low before the triangle formed) on the two-minute chart in the first two hours of the trading day.

    Once you have a specific set of entry rules, scan more charts to see if your conditions are generated each day. For instance, determine whether a candlestick chart pattern signals price moves in the direction you anticipate. If so, you have a potential entry point for a strategy.

    Next, you'll need to determine how to exit your trades.

    Deciding When to Sell

    There are multiple ways to exit a winning position, including trailing stops and profit targets. Profit targets are the most common exit method. They refer to taking a profit at a predetermined price level. Some common profit target strategies are:

    Strategy Description Scalping Scalping is one of the most popular strategies. It involves selling almost immediately after a trade becomes profitable. The price target is whatever figure means that you'll make money on the trade. Fading Fading involves shorting stocks after rapid moves upward. This is based on the assumption that (1) they are overbought, (2) early buyers are ready to take profits, and, (3) existing buyers may be scared away. Although risky, this strategy can be extremely rewarding. Here, the price target is when buyers begin stepping in again. Daily Pivots This strategy involves profiting from a stock's daily volatility. You attempt to buy at the low of the day and sell at the high of the day. Here, the price target is simply at the next sign of a reversal. Momentum This strategy usually involves trading on news releases or finding strong trending moves supported by high volume. One type of momentum trader will buy on news releases and ride a trend until it exhibits signs of reversal. Another type will fade the price surge. Here, the price target is when volume begins to decrease.

    In many cases, you will want to sell an asset when there is decreased interest in the stock as indicated by the ECN/Level 2 and volume. The profit target should also allow for more money to be made on winning trades than is lost on losing trades. If your stop-loss is $0.05 away from your entry price, your target should be more than $0.05 away.

    Just as with your entry point, define exactly how you will exit your trades before you enter them. The exit criteria must be specific enough to be repeatable and testable.

    Day Trading Charts and Patterns

    Three common tools day traders use to help them determine opportune buying points are:

  • Candlestick chart patterns, including engulfing candles and dojis
  • Other technical analysis, including trendlines and triangles
  • Volume
  • There are many candlestick setups a day trader can look for to find an entry point. If followed properly, the doji reversal pattern (highlighted in yellow in the chart below) is one of the most reliable ones.

    Image by Julie Bang © Investopedia 2019

    Also, look for signs that confirm the pattern:

  • A volume spike on the doji candle or the candles immediately following it, which can indicate that traders are supporting the price at this level
  • Prior support at this price level such as the prior low of day (LOD) or high of day (HOD)
  • Level 2 activity, which will show all the open orders and order sizes
  • If you use these three confirmation steps, you may determine whether or not the doji is signaling an actual turnaround and a potential entry point.

    Chart patterns also provide profit targets for exits. For example, the height of a triangle at the widest part is added to the breakout point of the triangle (for an upside breakout), providing a price at which to take profits.

    How to Limit Losses When Day Trading  Stop-Loss Orders

    It's important to define exactly how you'll limit your trade risk. A stop-loss order is designed to limit losses on a position in a security. For long positions, a stop-loss can be placed below a recent low and for short positions, above a recent high. It can also be based on volatility.

    For example, if a stock price is moving about $0.05 a minute, then you might place a stop-loss order $0.15 away from your entry to give the price some space to fluctuate before it moves in your anticipated direction.

    In the case of a triangle pattern, a stop-loss order can be placed $0.02 below a recent swing low if buying a breakout, or $0.02 below the pattern.

    You could also set two stop-loss orders:

  • Place an actual stop-loss order at a price level that suits your risk tolerance. Essentially, this level would represent the most money that you can stand to lose.
  • Set a mental stop-loss order at the point where your entry criteria would be violated. If the trade takes an unexpected turn, you'll immediately exit your position.
  • However you decide to exit your trades, the exit criteria must be specific enough to be testable and repeatable.

    Set a Financial Loss Limit

    It's smart to set a maximum loss per day that you can afford. Whenever you hit this point, exit your trade and take the rest of the day off. Stick to your plan. After all, tomorrow is another (trading) day.

    Test Your Strategy

    You've defined how you enter trades and where you'll place a stop-loss order. Now, you can assess whether the potential strategy fits within your risk limit. If the strategy exposes you to too much risk, you need to alter it in some way to reduce the risk.

    If the strategy is within your risk limit, then testing begins. Manually go through historical charts to find entry points that match yours. Note whether your stop-loss order or price target would have been hit. Paper trade in this way for at least 50 to 100 trades. Determine whether the strategy would have been profitable and if the results meet your expectations.

    If your strategy works, proceed to trading in a demo account in real time. If you take profits over the course of two months or more in a simulated environment, proceed with day trading with real capital. If the strategy isn't profitable, start over.

    Finally, keep in mind that if you trade on margin, you can be far more vulnerable to sharp price movements. Trading on margin means borrowing your investment funds from a brokerage firm. It requires you to add funds to your account at the end of the day if your trade goes against you. Therefore, using stop-loss orders is crucial when day trading on margin.

    Basic Day Trading Techniques

    Now that you know some of the ins and outs of day trading, let's review some of the key techniques new day traders can use.

    When you've mastered these techniques, developed your own personal trading styles, and determined what your end goals are, you can use a series of strategies to help you in your quest for profits.

    Although some of these techniques were mentioned above, they are worth going into again:

  • Following the trend: Anyone who follows the trend will buy when prices are rising or short sell when they drop. This is done on the assumption that prices that have been rising or falling steadily will continue to do so.
  • Contrarian investing: This strategy assumes a rise in prices will reverse and drop. The contrarian buys during a fall or short sells during a rise, with the express expectation that the trend will change.
  • Scalping: This is a style by which a speculator exploits small price gaps created by the bid-ask spread. This technique normally involves entering and exiting a position quickly—within minutes or even seconds.
  • Trading the news: Investors using this strategy will buy when good news is announced or short sell when there's bad news. This can lead to greater volatility, which can lead to higher profits or losses.
  • Which Trading Strategy Is Easiest for a Beginner?

    Following the trend is probably the easiest trading strategy for a beginner, based on the premise that the trend is your friend. Contrarian investing refers to going against the market herd. You short a stock when the market is rising or buy it when the market is falling. This may be a difficult trading tactic for a beginner. Scalping and trading the news require a presence of mind and rapid decision-making that, again, may pose difficulties for a beginner.

    Is Day Trading Good for Beginners?

    Most day traders will end up losing money, at least according to the data. But, with experience, your chances of succeeding can grow. Beginning traders should trade accounts with "paper money," or fake trades, before they invest their own capital in order to learn the ropes, test out strategies, and employ the tips above.

    Is Technical Analysis or Fundamental Analysis More Appropriate for Day Trading?

    Technical analysis can be more appropriate for day trading. That's because it can help a trader to identify the short-term trading patterns and trends that are essential for day trading.

    Fundamental analysis is better suited for long-term investing, as it focuses on valuation. The difference between an asset's actual price and its intrinsic value as determined by fundamental analysis may last for months, if not years. Market reaction to fundamental data like news or earnings reports is also quite unpredictable in the short term.

    That said, market reaction to such fundamental data should be monitored by day traders for trading opportunities that can be exploited using technical analysis.

    Why Is It Difficult to Make Money Consistently From Day Trading?

    Making money consistently from day trading requires a combination of many skills and attributes—knowledge, experience, discipline, mental fortitude, and trading acumen.

    It's not always easy for beginners to implement basic strategies like cutting losses or letting profits run. What's more, it's difficult to stick to one's trading discipline in the face of challenges such as market volatility or significant losses.

    Finally, day trading involves pitting wits with millions of market pros who have access to cutting-edge technology, a wealth of experience and expertise, and very deep pockets. That's no easy task when everyone is trying to exploit inefficiencies in efficient markets.

    Should a Day Trading Position Be Held Overnight?

    A day trader may wish to hold a trading position overnight either to reduce losses on a poor trade or to increase profits on a winning trade. Generally, this is not a good idea if the trader simply wants to avoid booking a loss on a bad trade.

    Risks involved in holding a day trading position overnight may include having to meet margin requirements, additional borrowing costs, and the potential impact of negative news. The risk involved in holding a position overnight could outweigh the possibility of a favorable outcome.

    The Bottom Line

    Day trading is difficult to master. It requires time, skill, and discipline. Many who try it lose money, but the strategies and techniques described above may help you create a potentially profitable strategy.

    Day traders, both institutional and individual, play an important role in the marketplace by keeping the markets efficient and liquid. With enough experience, skill-building, and consistent performance evaluation, you may be able to improve your chances of trading profitably.

    Applied Mathematics Bachelor of Science Degree

    Course Sem. Cr. Hrs. First Year CSCI-101

    Principles of Computing (General Education)

    This course is designed to introduce students to the central ideas of computing. Students will engage in activities that show how computing changes the world and impacts daily lives. Students will develop step-by-step written solutions to basic problems and implement their solutions using a programming language. Assignments will be completed both individually and in small teams. Students will be required to demonstrate oral and written communication skills through such assignments as short papers, homeworks, group discussions and debates, and development of a term paper. Lecture 3 (Fall).

    3 CSCI-141

     Computer Science I (General Education)

    This course serves as an introduction to computational thinking using a problem-centered approach. Specific topics covered include: expression of algorithms in pseudo code and a programming language; functional and imperative programming techniques; control structures; problem solving using recursion; basic searching and sorting; elementary data structures such as lists, trees, and graphs; and correctness, testing and debugging. Assignments (both in class and for homework) requiring a pseudo code solution and an implementation are an integral part of the course. An end-of-term project is also required. Lec/Lab 6 (Fall, Spring).

    4 MATH-181

    Calculus I (General Education – Mathematical Perspective A)

    This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals. (Prerequisites: MATH-111 or (NMTH-220 and NMTH-260 or NMTH-272 or NMTH-275) or equivalent courses with a minimum grade of B-, or a score of at least 60% on the RIT Mathematics Placement Exam. Co-requisites: MATH-181R or equivalent course.) Lecture 6 (Fall, Spring).

    4 MATH-182

    Calculus II (General Education – Mathematical Perspective B)

    This is the second in a two-course sequence. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates. (Prerequisites: C- or better in MATH-181 or MATH-181A or equivalent course.) Lecture 6 (Fall, Spring).

    4 MATH-199

    Mathematics and Statistics Seminar

    This course introduces the programs within the School of Mathematical Sciences, and provides an introduction to math and statistics software. The course provides practice in technical writing. Seminar 1 (Fall).

    1 YOPS-10

    RIT 365: RIT Connections

    RIT 365 students participate in experiential learning opportunities designed to launch them into their career at RIT, support them in making multiple and varied connections across the university, and immerse them in processes of competency development. Students will plan for and reflect on their first-year experiences, receive feedback, and develop a personal plan for future action in order to develop foundational self-awareness and recognize broad-based professional competencies. (This class is restricted to incoming 1st year or global campus students.) Lecture 1 (Fall, Spring).


    General Education – Elective


    General Education – First-Year Writing (WI)


    General Education – Artistic Perspective


    General Education – Natural Science Inquiry Perspective‡

    4 Second Year MATH-200

    Discrete Mathematics and Introduction to Proofs

    This course prepares students for professions that use mathematics in daily practice, and for mathematics courses beyond the introductory level where it is essential to communicate effectively in the language of mathematics. It covers various methods of mathematical proof, starting with basic techniques in propositional and predicate calculus and set theory, and then moving to applications in advanced mathematics. (Prerequisite: MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 3, Recitation 4 (Fall).

    3 MATH-231

    Differential Equations

    This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms. (Prerequisite: MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 3, Recitation 1 (Fall, Spring, Summer).

    3 MATH-251

    Probability and Statistics 

    This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications. (Prerequisites: MATH-173 or MATH-182 or MATH 182A or equivalent course.) Lecture 3, Recitation 1 (Fall, Spring, Summer).

    3 MATH-399

    Mathematical Sciences Job Search Seminar

    This course helps students prepare to search for co-op or full-time employment. Students will learn strategies for conducting a successful job search and transitioning into the work world. The course meets one hour each week for five weeks. Lecture 1 (Fall, Spring).

    0 STAT-257

    Statistical Inference

    Learn how data furthers understanding of science and engineering. This course covers basic statistical concepts, sampling theory, hypothesis testing, confidence intervals, point estimation, and simple linear regression. A statistical software package such as MINITAB will be used for data analysis and statistical applications. (Prerequisites: MATH-251. NOTE: Students cannot receive credit for both MATH-252 and STAT-257 nor for both STAT-205 and STAT-257.) Lecture 3 (Fall, Spring).

    3 Choose one of the following:



       Multivariable and Vector Calculus

    This course is principally a study of the calculus of functions of two or more variables, but also includes a study of vectors, vector-valued functions and their derivatives. The course covers limits, partial derivatives, multiple integrals, Stokes' Theorem, Green's Theorem, the Divergence Theorem, and applications in physics. Credit cannot be granted for both this course and MATH-219. (Prerequisite: C- or better MATH-173 or MATH-182 or MATH-182A or equivalent course.) Lecture 4 (Fall, Spring, Summer).


       Honors Multivariable and Vector Calculus

      Choose one of the following:



       Linear Algebra

    This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course. (Prerequisites: MATH-190 or MATH-200 or MATH-219 or MATH-220 or MATH-221 or MATH-221H or equivalent course.) Lecture 3 (Fall, Spring).


       Honors Linear Algebra


    General Education – Ethical Perspective


    General Education – Global Perspective


    General Education – Social Perspective


    General Education – Scientific Principles Perspective‡

    4 Third Year MATH-431

    Real Variables I

    This course is an investigation and extension of the theoretical aspects of elementary calculus. Topics include mathematical induction, real numbers, sequences, functions, limits, and continuity. The workshop will focus on helping students develop skill in writing proofs. (Prerequisites: (MATH-190 or MATH-200 or 1055-265) and (MATH-220 or MATH-221 or MATH-221H or 1016-410 or 1016-328) or equivalent courses.) Lec/Lab 4 (Fall, Spring).


    Program Electives


    General Education – Immersion 1, 2


    Open Electives


    General Education – Elective

    3 Fourth Year MATH-411

    Numerical Analysis

    This course covers numerical techniques for the solution of nonlinear equations, interpolation, differentiation, integration, and the solution of initial value problems. (Prerequisites: (MATH-231 and (MATH-241 or MATH-241H)) or MATH-233 or equivalent courses.) Lecture 3 (Fall).

    3 MATH-421

    Mathematical Modeling (WI-PR)

    This course explores problem solving, formulation of the mathematical model from physical considerations, solution of the mathematical problem, testing the model and interpretation of results. Problems are selected from the physical sciences, engineering, and economics. (Prerequisites: (MATH-220 or MATH-221 or 1016-410 or 1016-328) and MATH-231 and (MATH-241 or MATH-241H) and MATH-251 or equivalent courses.) Lecture 3 (Fall).

    3 MATH-441

    Abstract Algebra I

    This course covers basic set theory, number theory, groups, subgroups, cyclic and permutation groups, Lagrange and Sylow theorems, quotient groups, and isomorphism theorems. Group Theory finds applications in other scientific disciplines like physics and chemistry. (Prerequisites: (MATH-190 or MATH-200 or 1055-265) and (MATH-241 or MATH-241H) or equivalent courses.) Lec/Lab 4 (Fall, Spring).

    3 MATH-501

    Experiential Learning Requirement in Mathematics

    The experiential learning requirement in the Applied Mathematics and Computational Mathematics programs can be accomplished in various ways. This course exists to record the completion of experiential learning activities that have been pre-approved by the School of Mathematical Sciences. Such pre-approval is considered on a case-by-case basis. Lecture (Fall, Spring, Summer).

    0 MATH-606

    Graduate Seminar I

    The course prepares students to engage in activities necessary for independent mathematical research and introduces students to a broad range of active interdisciplinary programs related to applied mathematics. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Fall).

    1 MATH-607

    Graduate Seminar II

    This course is a continuation of Graduate Seminar I. It prepares students to engage in activities necessary for independent mathematical research and introduces them to a broad range of active interdisciplinary programs related to applied mathematics. (Prerequisite: MATH-606 or equivalent course or students in the ACMTH-MS or MATHML-PHD programs.) Lecture 2 (Spring).


    Math Graduate Core Electives


    General Education – Immersion 3


    General Education – Elective


    Open Electives

    6 Fifth Year MATH-790

    Research and Thesis

    Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor. (This course is restricted to students in the ACMTH-MS or MATHML-PHD programs.) Thesis (Fall, Spring, Summer).


    MATH Graduate Electives

    12 Total Semester Credit Hours



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    The Command Line

    1. Basic Shell

    The Linux command line, which is also known more properly as the shell, Now, the shell can be launched or started in a GUI window called a terminal program. Now, if you didn't have a GUI setup because you wanted to save on some resources, you can also login to the system locally using a text-based console. In addition to this, there's a shell that starts when you remotely log into a computer or a server if you're using a text-mode login protocol, something like Telnet or SSH. Now, the default shell in most Linux distributions is what's known as Bash, the "born again" shell. This is based on an older shell that was called the Born shell. Other shells are also available, but for the purposes of our time together in the lessons we're going to do, I'm going to be using the Bash shell.

    Most of the other shells are very similar to the Bash shell in functionality, but there are some subtle differences that do exist. Now, each Linux user account can specify their own default shell, so individual users can change their shells if they like a different one better. Now, this can be done with an account management tool such as the user mod, which we're going to describe in a future lesson. Most Linux distributions allow users to install various GUI terminal programmes as well. Typically, a desktop environment is going to come with its own terminal. So the terminal programme choices can depend on the desktop environment installed, whether that's KDE, Nome, Xfce, or something else. Now, many terminal programmes are going to include the word "terminal" in their name, although some don't. For example, in the KDE desktop environment, it's called Console or the generic X term. Now, the details of how to launch a terminal programme are going to differ from one desktop environment to another. So it's up to you to figure out how to do it in your particular environment.

    Normally, there's going to be an entry for the terminal in the desktop user menu or an icon on your desktop. Many desktop environments are also going to provide a search method where you can find the terminal program. For example, in Ubuntu's Unity desktop, you can click on the dash icon. This will show the Ubuntu symbol, and it's going to be located at the top of the application launcher, showing you a search box. If you type in the word "term," you're going to see the available terminal applications in the search results.

    Now, a much quicker way to launch a terminal is by using your keyboard shortcut. If you type Control-Alt, that will launch the terminal too. Most terminal programmes are going to support tabs, which are similar to the tabs you use in a web browser. Having multiple tabs open is really handy because it's going to allow you to run multiple programmes simultaneously, work easily in multiple directories, or run programmes both as a normal user and as an administrative root user. Now, root is the administrator account in Linux, and it gives the user elevated privileges not available to normal users. We're going to focus much more on the root account later on in the course, when we get to the section on users and groups.

    2. Command Line Syntax

    A computer's operation, no matter which operating system it's running, can be loosely described in just three steps. First, the computer waits for user input. Second, that user is going to select a command and enter it via the mouse or the keyboard. And third, the computer is going to execute that command command. Now, in Linux, the shell displays a prompt where commands can be entered using the keyboard. This prompt usually consists of a user and the host, which is your computer name, the current directory, and a final character.

    For Bash, that character is the dollar sign. A command is essentially a sequence of characters in a line, and you're going to end that line by pressing the enter key. Once you do that, that command is going to be evaluated by your shell. Now, many commands are vaguely inspired by the English language, and they form part of dedicated command syntax. Language commands in this language must follow certain rules known as "syntax" for the shell you're using. Now, if you use the wrong syntax, your computer is not going to be able to interpret them. To interpret the command line, the shell first tries to divide the line into individual words. Just like in real life, words are separated by spaces.

    Now, the first word on a command line is usually the actual command name. All of the other words on the line are parameters that will explain what you want to do in more detail. A command's parameters can be roughly divided into two types. We have parameters starting with a dash; these are known as options. Figuratively speaking, we call these switches, and they allow certain aspects of a command to be switched on or off. to pass several options to a command. They are frequently combined behind a single dash or typed out separately, as in "dash A," "space C." If you wanted to put them both together, you could do AC. Now, many programmes have more options than can be conveniently mapped to a single character. So they'll support long options for readability. And these long options most often start with two dashes, and they cannot be bundled together or accumulated. Now, the second thing we have are parameters without leading dashes, and these are known as arguments.

    These are often the names of files that the command should process. The general command structure can be seen as this: what do you want it to do? The option: how are you going to do it? And the arguments—what do I do with them? Usually, these options follow the command and proceed with the arguments. However, not all commands insist on this format. With some arguments and options, they can be mixed around arbitrarily, and they behave as if all the options came immediately after the command.

    With other commands, options are taken into account only when they are encountered while that command line is being processed in sequence, going from left to right. Now, just like in real life, Not properly using the correct syntax will lead to the system not understanding what you want done. It could either stop and do nothing, or it could cause severe consequences when the incorrect arguments or options are used. Now, later on, I'm going to show you a demonstration of how these commands are used with their corresponding syntax, and we'll break this down in more detail.

    3. Variables

    There are thousands of commands available for the command line user, and it's a monumental task to remember all of them. Now the real power of the computer is its ability to simplify repetitive and huge tasks for you, the user. To get it to do that, though, we have to create some power within the shell, and the shell allows us to automate things through the writing of shell scripts. Now, in the simplest terms, a shell script is a file containing a series of commands. The shell is going to read this file and carry out all the commands as if you'd been entering them directly on the command line itself. Now, a more in-depth discussion about shell scripting will be covered in our next videos coming up.

    But for now, let's talk about an essential feature of using the command-line interface. This feature gives you the ability to use a name or a label to refer to some other quantity, such as a value or a command. You may remember this from algebra class. It's known as a variable. Variables are used, at the very least, to make the machine code more readable. For users, however, variables can also come into use in more advanced programming or scripting. When the user is in a situation where you don't actually know the value before you execute the program, a variable is going to act as a placeholder that gets resolved at the actual execution time of your script.

    Variables are areas of memory that can be used to store information and are referred to by a name. Whenever the shell sees something that's written with a dollar sign and then a name, it assumes it's a variable, and it tries to find out what was assigned to that variable and substitute in the proper values. Now, to create a variable, a line is placed in a script that contains the name of the variable, followed immediately by an equal sign. No spaces are allowed here. After that equal sign, the information that needs to be stored is then going to be assigned. So, for example, if I wanted to set the age variable, I would put "dollar sign age equals 40" if I was saying that the age was set to 40 years old.

    Now, there are a few rules you need to know when naming your variables. First, variable names must start with a letter. Second, a name must not contain any embedded spaces. You can use underscores, though. So if I wanted to say the year of birth, I could put "year underscore of underscore birth," but I couldn't use spaces. Third, you cannot use any punctuation marks. That's it. Three simple rules: it starts with a letter, it can't have any spaces, and it can't have any punctuation. Now, when a user starts a shell session, some variables are already set by the startup file. To see all the variables that are in the user's environment, you're going to use the print env command, which stands for print environment. This will display all those environmental variables right on your screen, as you can see here. Now, I want you to remember that any time you see an uppercase variable where all the letters are uppercase, that is an environmental variable, just like you see here on the screen.

    4. Quoting

    In a previous lesson, we talked about how the shell interprets commands. The shell is going to read the input and find and run each command, passing the line arguments into the command to be executed. Now, the shell is going to treat a number of characters in a special way on the command line, and these characters are known as metaphorical characters.

    The most common shell meta character is the blank or space character, and this tells the shell to use separate arguments between those things. The shell does not pass any blanks or spaces to any command. Instead, the shell is going to use those blanks and spaces to separate and identify the individual arguments for that particular command. One blank separates arguments the same way ten or 100 blanks do, so any spaces are treated the same. Other shell meta characters include things like the dollar sign, the star, the semicolon, the greater-than symbol, the question mark, the ampersand, and the pipe.

    Now, "quoting" is the generic name given to the action of protecting shell metacaracters from being treated specially by the shell. A quoted blank does not separate arguments will.A will that is unquoted. A quoted semicolon doesn't separate commands the way that an unquoted semicolon does. Quoting is used to prevent the shell from acting on and expanding these meta characters. The quoting causes the shell to ignore that special meaning of the character, and instead, the character gets treated like plain text. This way, it can be used as part of an argument if it needs to be. Quoting is also done either with double quotes, single quotes, or backslash characters. While technically quoting is only used to protect individual shell metacaracters from the shell and not to the entire command line, it would look better to surround the entire argument with matching quote marks.

    Backslashes may also be used to quote or turn off that special character's ability, following each character one at a time. Quotes and backslashes tell the shell which parts of the input to treat as ordinary plain text characters and which to treat as special characters. The quoting delimits or identifies this string of characters, and the quoting mechanism is removed and is not part of the string that's passed to the command.

    Only the characters being quoted are going to be passed into that command. This allows the shell to remove the quoting mechanism before passing that delimited text as an argument back into the command and allowing it to be understood. So let's take a quick look at an example. Let's look at the phrase "hello, world." There's a command called echo, and when you type it, whatever comes after it on that line will be printed to the screen as a new line. So if I wanted to put "echo," "hello," and "semicolon world," I would have to type it out as "echo," "hello," and "semicolon world."

    Now, why did I need that backslash? Because if I didn't have it, what's going to happen is that the shell is going to think that a semicolon is used to execute two different commands: echo "hello" as one command and another called "world." But there is no command called "World." So it'll give you a syntax error. by using that backslash. It's going to treat that semicolon as plaintext, and it's going to put hello, semicolonworld, on the screen just like this. Let's take a look at one more example. Let's pretend you wanted to put $200 on the screen.

    Well, that's a pretty big phrase with a lot of spaces. So I'm going to type "echo" followed by a colon. I've moved the dollar sign back to 1200, quote. That way, I can put everything inside those quotes on the screen. And instead of that dollar sign being treated as a variable character because I have that backslash there, it's just going to print to the screen as normal plain text, as you can see here. Now, these are just two brief examples, but in the demonstration, we'll spend more time in the command line going over how we can quote and use backslashes to remove the special meaning from some of these characters and treat them as plain text.

    5. Proper Command Usage

    In this lesson, we're going to go through and learn a little bit more about the shell. I've talked about it in the last couple of videos, but now I want to show you how to use it hands on. There are a couple of ways to access your shell. The first way is to simply right-click on your desktop and click on "Open Terminal." If you do that, your shell will appear. Another way to do it is to go down to the application bar on your bottom left side, start typing in the word "term" or "terminal," and you'll get a lot of different options. One is already installed in my system, known as Terminal, but there are 15 more that I can get from the online Ubuntu store. You'll notice that things like Terminator, Terminator X, Docker, Copay, and many others are all in some way related to the term "term" or "terminal." And so if I continue to type, you'll see that I can get some different options, like Terminus, showing up here as well. Okay. But for me, the easiest way is to simply right-click and go to Open Terminal. This will bring up your default terminal that comes built into Ubuntu.

    From here, I'm going to go ahead and maximise my screen, and I'm going to go ahead and zoom in by hitting the CTRL, Shift, and plus signs two times to make it a little bit bigger and easier for you to see. Now, from here inside our shell, we're going to be able to go forward and start issuing commands. Now, as we talked about, we have to do this using the proper syntax. So let's pick a particular command to start playing with. I'm going to use the LS command, which stands for list. It's very similar to the Windows directory listing, or Dir command. Now to do this, I'm simply going to type in LS and hit Enter. If I do that, I get a list of the folders and files that are in the directory I'm sitting in. And I'm currently in the home directory.

    How do I know this? Well, because right before that dollar sign, you see the squiggly line or tilde. That tilde represents the home directory. Now if I wanted to go into one of these directories, for example, the Documents directory, I would type CD for change directory space and then the word Documents. If I hit Enter, you'll now see that I am in the home Documents directory. You can keep track of where you are based on that path that's showing up in light blue. Now, some distributions and some shells don't show you your current path. If you're in one of those distributions, you can always find out where you are by typing PWD and hitting Enter. That's PWD for "present working directory." Once you hit Enter, it will tell you the full path from the root all the way down to the folder you're in. In my case, my username, Home Dion Training, contains documents.

    Now, if I want to see what's inside the Documents folder, I can again type LS and hit Enter. By doing that, I got nothing back. Why is that? Well, let's take a look at the Documents folder. If we go into our files, we go into our documents. You'll see that it's an empty folder. That's why. because there's nothing there. Now, if we wanted to put some things there, we could use a couple of different commands. One of them is the command "Touch to UC." Touch will actually create an empty file with whatever file name you give it. So going back to our command Lexon, we talked about the fact that we have commands, options, and arguments. So the command is, "What do I want to do?" I want to touch a file and create it. Now, the option is: how do I want to do it? And the argument is, what do I do it with? Well, with the Touch command, I actually don't need an option.

    So I'm just going to go right into the argument. And what I want to do it with is going to be the name of the file. In my case, I'm going to call it Test One TXT. If I hit Enter and now I hit LS, I can then see if it's in the directory. And you can see we now have that file inside the directory. One of the things you're going to want to do as we move forward is create some folders and files that we can play with as we go through and do things like copying, moving, renaming, and deleting files and folders in our next series of lessons. As we get deeper into the shell, let me go ahead and switch back to the GUI, because you can also do this by right-clicking and selecting "New Folder." And so I can call this folder One, and then I'll create another one called Folder Two.

    Now if we go back to our terminal, we can go ahead and create Touch Test Two TXT as well. And if I hit LS, I should see four things listed. I now have Test One dot TXT folder one. and TXT two dots test Now, we talked about the fact that there are options as well. What do you want to do with the list command besides just listing out the names? Well, maybe you want to be able to see additional details and additional information about these files and folders. For example, maybe you want to know how big they are, what they contain, and other things like that. Well, if we do LS-DA, that will actually list it out with additional details. So here you can see on the left side that we have the permissions, we see the username of who owns it, in this case, Dion Training, and we can see the file size.

    If you look at tests one and two, they are each zero bytes big. Now, why are they zero bytes? because all we did was create an empty file. We didn't put anything in that file. And so if I want to change that, let me go back over here to my file system, and I'm going to open up a test one. And I'm just going to add something like this as a test, and then I'm going to go ahead and save it and close it. Now, if we go back and type LS la, we should see that test one is no longer zero bytes.

    And in fact, you can see it now has 16 bytes of data, which is still a very small file. But we can see that information has been saved in there, and there is now a file size associated with it. So at this point, we've seen how to use some basic commands like touch and LS. When we use things like Touch, we use it with an argument that says, "Touch this file, test one, and test two." When we used LS, we used it with some options, and we turned them on and off using that dash command. So in this case, I wanted to see the big picture with all of the attributes. So it's LSLA. Don't worry too much about the commands I'm using in this particular lesson yet. We're going to dive into each of these commands in much more detail later on. Now, another thing we talked aboutwas variables and variable names.

    And I had mentioned that we can use the print env command to print out our environmental variables. Well, let's go ahead and do that and see what we have. Here we go. And you can see that at the bottom, the last thing there is "old PWD," which is the old present working directory. It's set to home demon training, as you can see. Now why is that? Well, if you remember from earlier, we started out in the home deauctraining directory, and then I changed directories into documents. And when I did that, there was an environmental variable that stored the last directory you were in. That's known as "old TWD."

    And so again, if I want to go back up and say, "CD space dot dot," that will take me up one directory. Now I am back in the home DEON training directory. That's what the tilde stands for. Now, if I print my environmental variables again, what do you think that old PWD is going to say? It should read home-based training materials. Let's see if it does. And there it is. So you can see how it keeps track of the last directory you were in by using this environmental variable. That's just one of many different variables that we have as far as our environmental variables, shown here on the screen. The last thing I wanted to discuss here while we're in the terminal is the concept of quoting. And we talked about the fact that we need to use quoting if we want to turn off some kind of special meaning for a character.

    For example, we have the character "semicolon." Now on the command line, the semicolon will allow you to enter two commands on one line. So, for example, we have the command "echo," which will print something to the screen like "hello." And so if I just hit enter, you'll see "Hello" show up. Now, if I wanted to do echo, have hello show up, and then show a directory listing like LS, I wanted to do them both at the same time. I can do that by typing echo, hello, a semicolon, and then LS; that semicolon has a special meaning of doing both of these commands and then displaying them on the screen.

    And so there we go. We now have "hello," and then we have the list of folders inside this directory. Now, what would I do if I wanted to put something on the screen, like, "My name is Jason, and I live in DC"? Now, because I have a semicolon there and I want to print that to the screen, I need to escape that character. And so what I'm going to do here is echo this to the screen because that's the command I want. I'll put it all inside quotes. And so you'll see here, because I have quotes around everything, that the semicolon is treated as a regular character and not a special character. Now, let's do that again, but let's take away the quotes. Now, what do you think is going to happen? Well, it should treat this as an echo; my name is Jason. End that command and then start the new command, which it thinks is called I for "I live in DC." As a result, we'll probably get an error saying that "I" isn't a valid command. Let's go ahead and hit enter.

    And that's exactly what happened. Now, what if I don't want to use those quote marks around everything? Well, I can still use that semicolon, but I have to escape its meaning. And if you remember from the lesson, we can do that by using the backslash. So now it's going to be treated as one long command. Echoing the phrase, my name is Jason Semicolon. I live in Washington, DC. If I hit enter, you'll see that that gives me the same thing as using those quote marks. Again, there are lots of different ways to do quoting. You can use quote marks. You can use the backslash. It really is up to you and which one you're more comfortable with. Personally, I tend to use the quote marks a whole lot more than the backslashes, but the backslash is a valid way to do it as well.

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