聚合文章

I’ve read a lot of articles on Traditional vs Roth IRA. One can do a serious mathematical analysis of which one is better, given that you want to invest a total of x income into the account for a particular year. Money in excess of x will be put in a normal investment account. There is a widely held…

Chao Xu

Word break with cost

Problem1 Given a set of strings W, a cost function c:W\to \R and a string s. Find elements w_1,\ldots,w_k\in W such that s=w_1\ldots w_k, and \sum_{i=1}^k c(w_i) is minimized. This problem is a generalization of the word break problem on leetcode. Many algorithms you see online assumes that each str…

Chao Xu

Bounds on number of cuts

Consider we have an undirected graph G=(V,E) of n vertices, and there are positive cost c:E\to \R^+ on the edges. We define c(F)=\sum_{e\in F}c(e), to be the cost (value) of F\subset E. Let \mathcal{P} be a partition of V where each partition class is non-empty. We define E(\mathcal{P}) to be the se…

Chao Xu

Maximize Cash Back

Credit cards often offers rewards for purchases. For example, a card that gives 5% cash back for grocery stores. Also, credit cards often can be used to buy gift cards for specific stores. For example, one can use Chase Ink Cash (CIC) and go to Staples and buy gift card for Amazon for effectively 7.…

Chao Xu

The value of a gift card in beancount

I’m using beancount to do accounting. In beancount, you are allowed to have commodities. One can view gift card as commodity, but also as a currency. Say, I bought an $100 Amazon gift card for $90, I would write 100 AMAZON {0.9 USD}, which means 100 units of Amazon with unit cost $0.9. Later on, I u…

Chao Xu

Yotta Savings and covering designs

Yotta Savings is a FDIC insured savings account that gives you “interest” in another way. It has a 0.2% APR. It is much better than the APR of many banks, but much worse than actual high APR savings accounts, e.g. Marcus, Ally. However, for each $25, Yotta gives you a ticket weekly to their drawing,…

Chao Xu

Test conjectures on $k$-partitions over submodular functions

This article considers tools one can use to quickly test conjectures. I work in combinatorial optimization, and often there are cases where one can phrase a problem as a conjecture over a finite domain. Testing conjectures using brute force quickly becomes infeasible due to combinatorial explosion. …

Chao Xu

The related employer controlled group

Disclaimer: Not an accountant nor a lawyer. For employees in the US, employers (not just the employee) can contribute to the employee’s retirement fund 401(k). There is an maximum limit. It is M = \$61,000 for 2022. If a person works for multiple unrelated employers, each employer, in theory, can co…

Chao Xu

Use a box spread as a line of credit

In an idealized world, you could borrow at the Effective Federal Funds Rate (EFFR) and also earn roughly the same rate on cash deposits. For simplicity, assume the relevant short rate is fixed for a month. Let’s say it turns out to be 10% per month. Assume the stock will rise by 20% that month. In r…

Chao Xu

AI Agents for the Working Mathematician

REVISED 2026-09-19. This is a living document. I revise it as the mathematical AI frontier changes and as experience with these systems changes what we know about using them for mathematics. The recommendations below describe current practice and will keep changing. Most working mathematicians I tal…

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