These are some of the econ course offered at schools I listed with mathematical economics majors or tracks:
Games & Strategies in Economics (prereq: calculus, single var)
Linear Optimization and Game Theory (prereq: linear algebra)
Economic Statistics with Calculus
Economic Statistics (prereq: calculus, multi var)
Mathematical Economics (prereq: calculus, multi var)
Microeconomic Theory (prereq: calculus, multi var)
Econometrics (prereq: multivar calculus / linear algebra)
Applied Econometrics ((prereq: calculus, probability)
To the extent one can tell from the brief online descriptions, some of these schools do seem to be offering math-oriented economics courses.
The schools I listed are just the first few that showed up in a search for “mathematical economics” majors/tracks. Do they consistently offer a richer variety of such courses than colleges that don’t offer such a program? I really don’t know; maybe this is indeed a silly distinction. Macalester College is an example of a school that has a high economics PhD production rate (per Siegfried & Stock 2006). Although it does not offer a distinct “mathematical economics” program/track, it does require all econ majors to take multivariable calculus and statistical modeling courses. At least one of these (or linear algebra) is a prerequisite to some advanced econ courses at Macalester. For example, an Intro to Econometrics course requires both multivariable calculus and statistical modeling as prerequisites. An Empirical Finance course requires multivar calc and linear algebra as prerequisites.
Then there is the possibility that some student projects involve a fair amount of sophomore level (or higher) mathematics (irrespective of the course prereqs). I’m guessing some of the following econ department theses at Reed College did.
An examination of rational speculative bubble models: Early rational bubble models, herding, and heterogenous beliefs
Predictive validity of the new SAT reasoning test
Markov chain Monte Carlo and the Black-Scholes formula
Interest rates and deficit expectations using real-time data
Prediction and parameter estimation in the presence of missing data
Creative destruction in a dynamic stochastic general equilibrium framework : evaluation through calibration and simulation
Time-varying risk premia and the euro: A state-space model
Zipf’s law and international integration: An exploration of the rank-size distribution for cities
Financial systemic risk : classification and measurement
On simulating a new Keynesian dynamic stochastic general equilibrium model: Replicating Smets and Wouters
Reed ranked #5 in Siegfried & Stock’s Economics Program-Size Normalized Top American Sources of
Eventual Economics Ph.D.s, 1997-2003. Nevertheless, its economics department has no formal mathematics requirement.