Introduction

This chapter begins by showing why college is so consequential to Americans’ lives. It then describes how and why the US education system is stratified by social class. The road to college, especially a selective college, is much smoother for those who come from more affluent and educated families. The farther down on the socioeconomic ladder you go, the bumpier and steeper the climb to college becomes. Social class matters to children’s schooling because parents’ childrearing strategies continue to influence children even after they leave home. Yet the current narratives that we have about adolescents do not reflect their religious upbringing. The chapter introduces a new childrearing logic that cuts across social class groups and accounts for the role of religion: “religious restraint.” This chapter also describes the state of religion in America and explains why this book is primarily about “abiders”—Christians who display high degrees of religiosity.

Living for God

This chapter introduces readers to the childrearing logic of “religious restraint” and distinguishes it from Annette Lareau’s classic class-based childrearing strategies of “concerted cultivation” and “natural growth.” Deeply religious families do not fall into either of Lareau’s categories. Parents who raise their children with religious restraint exist across different social class groups. Children raised with religiously restraint (“abiders”) come to believe in God so deeply that it alters their sense of self—their idea of who they are. Teens believe that they are constantly being evaluated by God, which prompts them to change how they perceive themselves, how they carry themselves, and how they imagine their future selves. Living to please God shapes how teens see themselves and how they behave, which the chapter describes as developing a “God-centered self-concept.” Teens raised with religious restraint who develop a God-centered self-concept come from different genders, social class backgrounds, racial backgrounds, and religious traditions.

Galois covers of ℙ1 and number fields with large class groups

For each finite subgroup [Formula: see text] of [Formula: see text], and for each integer [Formula: see text] coprime to [Formula: see text], we construct explicitly infinitely many Galois extensions of [Formula: see text] with group [Formula: see text] and whose ideal class group has [Formula: see text]-rank at least [Formula: see text]. This gives new [Formula: see text]-rank records for class groups of number fields.

L-algebras and topology

[Formula: see text]-algebras are based on an equation which is fundamental in the construction of various torsion-free groups, including spherical Artin groups, Riesz groups, certain mapping class groups, para-unitary groups, and structure groups of set-theoretic solutions to the Yang–Baxter equation. A topological study of [Formula: see text]-algebras is initiated. A prime spectrum is associated to certain (possibly all) [Formula: see text]-algebras, including three classes of [Formula: see text]-algebras where the ideals are determined in a more explicite fashion. Known results on orthomodular lattices, Heyting algebras, or quantales are extended and revisited from an [Formula: see text]-algebraic perspective.