Steven Jang
Software Engineer
I am a software engineer based in Los Angeles, CA specializing in web/mobile applications
Technologies
Frontend
JavascriptTypescriptReactReact NativeReduxNextJSGatsbyBackend
GolangDockerGCloudAWSRabbitMQgRPCFirebaseBashJavaGraphQLRESTKubernetesExpressMisc
RegExGit & GithubLaTexPythonEducation
Cal Poly Pomona
Major: Computer ScienceMinor: Mathematics
GPA: 3.62
Papers
The Pentagon: 881
Recursion Theory
Find a formula (possibly recursive) for the number of integers with n digits that contain exactly one 47 in the integer.
See my solutionThe Pentagon: 885
Inequalities and Infinite Series
$$a,b,x,y > 0, n \in \mathbb{N}^*$$ prove that $$\frac{(x+y)^n}{2^{(n - 1)}} \leq \frac{(ax+by)^n +(bx+ay)^n}{(a +b)^n} \leq x^n +y^n$$
See my solutionThe Pentagon: 882
Functional Equations
Find all functions $$f: \mathbb{R}\xrightarrow{}\mathbb{R}$$ $$f(x^4+y) = f(x) + f(y^4)$$ $$x,y \in \mathbb{R}$$
See my solutionThe Pentagon: 889
Infinite Series
$$\displaystyle h_n = \sum_{k=1}^{2n}\frac{(-1)^{k+1}}{k}$$ Identify: $$\lim_{n\to\infty}({\log(2)-h_n})n$$ $$\lim_{n\to\infty}({(h_n h_{n+1}-\log^2(n))n})$$
See my solutionCrux: 1377
Infinite Series
Consider a decreasing and positive sequence $$\{{a_{2k-1}}\}_{k\geq{1}}$$ whose sum converges. Prove there exists another decreasing and positive sequence $$\{a_{2k}\}_{k\geq{1}}$$ such that the combined sequence $$\{a_{n}\}_{n\geq{1}}$$ is decreasing and the series $$\sum_{n=1}^{\infty}{a_n}$$ converges to an irrational number
See my solution