Computer Science
Embark on a comprehensive self-learning journey in Computer Science, inpsired by college-level programs. Achieving mastery in this pathway demands a dedicated commitment, and the process may span several years. This pathway involves many content areas, including programming, algorithms, data structures, software development methodologies, databases, and computer architecture. Hands-on coding projects and collaborative learning will be integral to the process. Networking with fellow learners, participating in online communities, and seeking mentorship from experienced professionals will enhance the learning experience. Regularly applying learned concepts in practical scenarios and staying updated with industry trends will be crucial; you must build projects. Embracing a growth mindset, resilience, and continuous curiosity are key attributes for success in this self-learning path.
What will you learn?
Below, you can find a list of competencies that describe what skills and knowledge you will need to progress through your pathway. You can proove that you have mastered the competencies below by uploading artifacts (called 'proofs') to act as proof of your skills and knowledge.
Calculus
Graph Functions
Graph functions including linear, quadratic, exponential, logarithmic, and trigonometric functions.
Interpret graphs of functions and their transformations.
Given a graph of a function, correctly identify the function and its transformations.
Evaluate limits algebraically and graphically
Calculate limits of functions including rational functions, trigonometric functions, and piecewise functions. Explain the connection of limits and continuity.
Compute derivatives using basic rules
Differentiate functions using the sum rule, product rule, quotient rule, and chain rule. Apply these rules systematically to various types of functions.
Apply derivatives to solve real-world problems
Use derivatives to analyze rates of change in real-world contexts such as motion, population growth, and economics. Solve optimization problems by finding critical points and classifying them using the first and second derivative tests.
Find areas under curves using integration
Compute the area enclosed by curves by setting up definite integrals over appropriate intervals. Interpret the result geometrically as the area under the curve.
Calculate the average value of a function over an interval
Determine the average value of a function over a closed interval by computing the definite integral of the function over that interval and dividing by the length of the interval.
Solve problems involving accumulation and motion using integration
Apply integration to solve problems related to accumulation, such as finding total distance traveled or total amount accumulated over time. Use integration to analyze motion by computing displacement, velocity, and acceleration functions.
Differentiate and integrate transcendental functions
Apply differentiation techniques to find derivatives of trigonometric, exponential, and logarithmic functions. Integrate transcendental functions using appropriate techniques such as trigonometric substitution and integration by parts.
Apply differentiation and integration techniques
Utilize advanced techniques such as implicit differentiation, logarithmic differentiation, and trigonometric substitution to differentiate and integrate functions efficiently.
Analyze convergence and divergence of sequences and series
Determine convergence or divergence of sequences and series by applying various convergence tests such as the ratio test, root test, and comparison tests. Identify alternating series and demonstrate understanding by applying the alternating series test.
Compute Taylor and Maclaurin series expansions
Compute Taylor polynomials and Maclaurin series expansions for functions centered at a given point. Demonstrate proficiency in generating accurate series expansions to approximate functions.
Apply Taylor and Maclaurin series expansions
Apply Taylor and Maclaurin series expansions to approximate functions and estimate function values. Illustrate proficiency by accurately using series expansions in real-world or mathematical contexts.