I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips.

Investopedia contributors come from a range of backgrounds, and over 25 years there have been thousands of expert writers and editors who have contributed. Amilcar has 10 years of FinTech, blockchain, ...

Lucas Downey is the co-founder of MoneyFlows, and an Investopedia Academy instructor. Michael Boyle is an experienced financial professional with more than 10 years working with financial planning, ...

Apr. 27, 2026 A mysterious “golden orb” found more than two miles deep in the Gulf of Alaska left scientists baffled for over two years, sparking wild speculation about its origins. After an intensive ...

Need to scan, copy, or fax, in addition to printing? An AIO printer is what you want. Find the right multifunction machine based on our in-depth reviews and expert advice. Most of my current work for ...

Salmon provides essential nutrients like omega-3 fatty acids, protein, B vitamins, selenium, and potassium. These nutrients can support heart health, brain function, and bone strength — among other ...

Abstract: In this paper, we define the Windowed Octonion Quadratic Phase Fourier Transform (WOQPFT) and derive its inversion formula, including its essential properties, such as linearity, ...

Abstract: Current state-of-the-art plug-and-play countermeasures for mitigating adversarial examples (i.e., purification and detection) exhibit several fatal limitations, impeding their deployment in ...

differentiation for periodic functions in 1D, 2D, and 3D domains. plt.plot(x_np, dfdx[0].squeeze().cpu().numpy(), label="Fourier dfdx") plt.plot(x_np, np.cos(x_np ...

The tutorial covers both FC-Legendre and FC-Gram methods for 1D, 2D, and 3D data.