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The American Mathematical Society Software Engineer Interview Guide

The American Mathematical Society Software Engineer interview guide: reported rounds, questions and how candidates describe the process.

The 60-second brief

A Software Engineer at The American Mathematical Society plays a pivotal role in bridging the gap between complex mathematical research and digital infrastructure. You are responsible for developing and maintaining the platforms that support the dissemination of mathematical knowledge, ensuring that researchers, educators, and students have seamless access to vital data and publications. Your work directly impacts the global mathematical community by building robust, scalable software that powers the organization's digital ecosystem. This role is unique because it combines standard software engineering rigor with the specific needs of a scholarly and academic environment. You will often work closely with subject matter experts, including professors and researchers, to translate intricate requirements into functional digital solutions.

This guide is scoped to a Software Engineer candidate at The American Mathematical Society.

Focus areas

  • Core Java
  • Java 8 (Java 1.8)
  • Spring Boot

The The American Mathematical Society interview process

The American Mathematical Society candidates report 5 rounds over 4-6 weeks. The stages below are what candidates describe, not a published process.

Initial Assessment

Candidates undergo an initial assessment to evaluate their technical skills.

What to demonstrate

  • Candidates undergo an initial assessment to evaluate their technical skills
  • Depth in Core Java

How to prepare

  • Answer aloud and timed: How would you describe your competency level in [Primary Language, e.g., Java]?
  • Answer aloud and timed: Can you explain the difference between specific features in Java 8 and later versions?

Technical Interviews

Multiple technical interviews focusing on deep technical understanding and specific skills.

What to demonstrate

  • Multiple technical interviews focusing on deep technical understanding and specific skills
  • Depth in Core Java

How to prepare

  • Answer aloud and timed: What is your experience with modern web frameworks like Angular or backend frameworks like Spring Boot?
  • Answer aloud and timed: How do you handle database connectivity or integration within a microservices architecture?

Panel Discussions

Candidates participate in discussions with various stakeholders, including hiring managers.

What to demonstrate

  • Candidates participate in discussions with various stakeholders
  • Including hiring managers

How to prepare

  • Answer aloud and timed: Can you explain how you would implement a specific feature using HTML, CSS, and Bootstrap?
  • Answer aloud and timed: Can you walk through a past project that you found particularly challenging?

Cultural Fit Conversations

Conversations with leadership to assess alignment with the organization's mission.

What to demonstrate

  • Conversations with leadership to assess alignment with the organization's mission
  • Depth in Core Java

How to prepare

  • Answer aloud and timed: How do you approach the design of a software component from scratch?
  • Answer aloud and timed: Have you worked on projects involving binary trees or similar data structures?

Final Panel Interviews

Final round of interviews where technical rigor is assessed before making a decision.

What to demonstrate

  • Final round of interviews where technical rigor is assessed before making a decision
  • Depth in Core Java

How to prepare

  • Answer aloud and timed: How do you handle debugging and performance optimization in a production environment?
  • Answer aloud and timed: Where do you see yourself in five years?

Where candidates lose points

Understand the Mission

Spend time on the American Mathematical Society website. Understanding the organization’s role in the mathematical community will help you answer "why us" questions with sincerity.

Be Ready for Panel Interviews

You may face a panel of interviewers, including department heads. Maintain eye contact, address each person in the room, and stay professional even if the line of questioning feels intense.

Prepare Your Portfolio

Be ready to discuss the specific technologies you used in your past projects, even if they aren't exactly the ones used at the American Mathematical Society. Focus on the transferable skills.

Stay Calm Under Pressure

If you encounter a technical question you don't know, explain your thought process for arriving at a solution rather than guessing.

Questions & practice

How would you describe your competency level in [Primary Language, e.g., Java]?

Medium · Technical Competency and Language Profic

Approach

  1. Say what the runtime actually does before reasoning about the code.
  2. Name what is shared across threads and what owns each piece of state.
  3. Identify the window where an invariant is briefly untrue.
  4. Distinguish a value from a reference to it, and say which one you handed out.

Follow-up

  • What happens if two callers reach this at the same time?
  • Where could this allocate more than you expect?

Can you explain the difference between specific features in Java 8 and later versions?

Medium · Technical Competency and Language Profic

Approach

  1. Say what the runtime actually does before reasoning about the code.
  2. Name what is shared across threads and what owns each piece of state.
  3. Identify the window where an invariant is briefly untrue.
  4. Distinguish a value from a reference to it, and say which one you handed out.

Follow-up

  • What happens if two callers reach this at the same time?
  • Where could this allocate more than you expect?

Can you explain how you would implement a specific feature using HTML, CSS, and Bootstrap?

Medium · Technical Competency and Language Profic

Approach

  1. Say what the runtime actually does before reasoning about the code.
  2. Name what is shared across threads and what owns each piece of state.
  3. Identify the window where an invariant is briefly untrue.
  4. Distinguish a value from a reference to it, and say which one you handed out.

Follow-up

  • What happens if two callers reach this at the same time?
  • Where could this allocate more than you expect?

Can you walk through a past project that you found particularly challenging?

Medium · Project Experience and Problem Solving

Approach

  1. Restate the input: its shape, its size, and what is guaranteed about it.
  2. Name the brute-force solution and its complexity before improving on it.
  3. Choose the data structure from the access pattern, not from familiarity.
  4. State the target complexity and say which constraint rules the naive version out.

Follow-up

  • How does this change if the input no longer fits in memory?
  • What is the worst case, and how likely is it on real data?

How do you approach the design of a software component from scratch?

Medium · Project Experience and Problem Solving

Approach

  1. Restate the input: its shape, its size, and what is guaranteed about it.
  2. Name the brute-force solution and its complexity before improving on it.
  3. Choose the data structure from the access pattern, not from familiarity.
  4. State the target complexity and say which constraint rules the naive version out.

Follow-up

  • How does this change if the input no longer fits in memory?
  • What is the worst case, and how likely is it on real data?

Have you worked on projects involving binary trees or similar data structures?

Medium · Project Experience and Problem Solving

Approach

  1. Restate the input: its shape, its size, and what is guaranteed about it.
  2. Name the brute-force solution and its complexity before improving on it.
  3. Choose the data structure from the access pattern, not from familiarity.
  4. State the target complexity and say which constraint rules the naive version out.

Follow-up

  • How does this change if the input no longer fits in memory?
  • What is the worst case, and how likely is it on real data?

Explain why the owner filter ignores the listing index

Medium · composite index · query plans · sort elimination

The only index on resource is (tenant_id, status, updated_at DESC, resource_id DESC). A new endpoint returns one user's resources across all statuses, newest created first: WHERE tenant_id = $1 AND owner_user_id = $2 ORDER BY created_at DESC LIMIT 20. On a tenant with 2M rows it takes 900 ms and EXPLAIN shows a sort above a large scan. Explain precisely why the existing index cannot serve it, give the index that can, and state which of these the new index still will not help: owner_user_id alone across tenants; the same query ordered by updated_at. PostgreSQL 16.

Approach

  1. Separate the two jobs an index does. For filtering, a composite btree is seekable only on a left prefix, so with no predicate on status the scan can at best range over tenant_id and test owner_user_id per row; PostgreSQL 16 has no btree skip scan to jump the unconstrained column.
  2. For ordering, the index is sorted by (status, updated_at) within a tenant and not by created_at, so the LIMIT cannot stop early: every matching row is read and then sorted. That is the 'Sort Method: top-N heapsort' line, and it is why the plan reads 2M rows to answer with 20.
  3. Derive the replacement from the access path — equality, equality, then the ordering column: CREATE INDEX CONCURRENTLY ON resource (tenant_id, owner_user_id, created_at DESC). The scan seeks to the (tenant, owner) range and walks 20 entries in order, so the Sort node disappears along with the row-read.
  4. Treat INCLUDE (title, status) as conditional, not free. An index-only scan still visits the heap for any row whose page is not marked all-visible, so on a table taking 1.2k writes/second the win depends on autovacuum keeping the visibility map current, and the wider index costs more on every insert.

Follow-up

  • 90% of rows are status='active'. Would a partial index WHERE status = 'active' change your answer, and for which of the three queries?
  • A dashboard runs this for 40 owners in one page load. What changes about the design?

Hold a per-tenant active cap against concurrent creates

Hard · write skew · isolation levels · constraints

A tenant on the standard plan may hold at most 50 resources with status='active'. The create handler runs SELECT count(*) FROM resource WHERE tenant_id = $1 AND status = 'active', compares to 50, then inserts. Two creates arrive 3 ms apart on different instances and the tenant lands at 51. Name the anomaly, say whether PostgreSQL 16 READ COMMITTED or REPEATABLE READ prevents it and why, then give an implementation that holds the cap at READ COMMITTED with the exact statements. Finally, say what changes when the cap is 'at most one running export per tenant' on job_run.

Approach

  1. Name it: write skew. The two transactions read an overlapping set and write disjoint rows, so there is no row-level conflict for the engine to detect and each commit is individually legal.
  2. Rule out the levels precisely. READ COMMITTED takes a fresh snapshot per statement and takes no lock on the counted rows, so both see 49. PostgreSQL's REPEATABLE READ is snapshot isolation: it removes non-repeatable reads and phantoms within the snapshot but still admits write skew, because the anomaly is not a re-read of a changed row, it is a read of a set that a concurrent transaction invalidates. Only SERIALIZABLE closes it, by tracking the read dependency and aborting one transaction with SQLSTATE 40001 — a guarantee that exists only if the application re-runs the whole transaction from the read.
  3. Convert the set predicate into a single-row conflict: keep tenant.active_resource_count and run UPDATE tenant SET active_resource_count = active_resource_count + 1 WHERE tenant_id = $1 AND active_resource_count < 50 in the same transaction as the INSERT. Zero affected rows is the cap, returned as 409. The row lock serialises the decision at any isolation level, and contention is bounded to one tenant's row — which is also the fair-scheduling unit, unlike a global counter that would convoy every tenant behind one row.
  4. State the cost you just took on: a counter is a second source of truth that can drift, so every path that changes status must adjust it inside the same transaction, and a periodic reconciliation has to exist, with resource_revision as the authority for what the count should have been.

Follow-up

  • A resource moves from archived back to active. Which statements change, and what breaks if the counter update and the status change land in different transactions?
  • The cap becomes plan-dependent and a plan can change mid-month. Where does the number 50 live, and who reads it?

How do you handle database connectivity or integration within a microservices architecture?

Medium · Technical Competency and Language Profic

Approach

  1. Fix the scope first: who calls this, how often, and what they do when it fails.
  2. Name the read and write paths separately; they rarely have the same bottleneck.
  3. Choose a partition key and say what query it makes expensive.
  4. State the consistency you need, and where you are willing to be stale.

Follow-up

  • What breaks first when traffic grows ten times?
  • How does this behave when that dependency is down for an hour?

Shard by tenant when one tenant outgrows a single shard

Hard · sharding · hot partition · routing

One primary holds resource, resource_revision, outbox_event and idempotency_key for every tenant and is at its write ceiling at 1.2k writes/second. tenant_id leads every index. Shard across eight primaries. One tenant holds 22% of all rows and by itself exceeds a single shard's write capacity. Design the routing, the split of that tenant, and the online move of a tenant between shards with writes continuing. State what breaks for queries that are tenant-scoped today, and exactly what a write must do when it arrives at the old shard after the cutover.

Approach

  1. Route on a unit smaller than a tenant from the start. Make the routing key (tenant_id, bucket) with a fixed bucket count - 64 over eight shards - and keep a directory mapping each (tenant_id, bucket) to a shard, carrying a version and cached in every service. An ordinary tenant has all 64 buckets pointing at one shard and behaves exactly as it does today; only the hot tenant has its buckets spread. Hashing tenant_id alone spreads tenants evenly, gives you no way to move one, and has no answer at all for a tenant larger than a node. The bucket count is the part you cannot change later without rehashing rows, so pick it well above the shard count and rebalance by moving buckets, not by re-bucketing.
  2. For the tenant that exceeds one node, its buckets must land on different shards - that is the whole point of bucketing it, and buckets confined to its own shard would rename the rows while leaving every write on the node whose ceiling it already exceeds. Size it from measured numbers rather than from its row share: 22% of rows says nothing about write rate. The current primary tops out near 1.2k writes/second on this hardware and workload, so a tenant peaking at W writes/second needs its buckets spread over at least ceil(W / headroom-per-shard) shards, where the divisor is the share of each shard's ceiling you are willing to give it while that shard still serves other tenants - not the full 1.2k. Size on its peak, not its mean.
  3. Fix the co-location invariant at the right grain. What must commit in one transaction is a resource, its resource_revision row and its outbox_event row, so the bucket is a property of the resource: derive it once at creation and stamp it into resource_id, and every later revision and event routes with its parent for free. Per-tenant co-location was never the requirement, and mistaking it for one is what makes a tenant look unsplittable. What genuinely breaks is an invariant spanning two resources of one tenant - a per-tenant counter, uniqueness across its resources - which now needs either a home-shard table or two-phase commit, and 2PC at this write rate is not a serious option.
  4. Keep the idempotency constraint arbitrating, because it is now enforced per shard. PRIMARY KEY (tenant_id, idempotency_key) only continues to reject a retry if the same key always lands on the same shard, so derive the create-path bucket from hash(tenant_id, idempotency_key) and mint the new resource_id inside that bucket, which also puts the key row and the resource it guards in one transaction. A bucket chosen from anything that differs between a request and its retry - a timestamp, the worker id, a client-supplied resource id - splits one key across two shards, both inserts succeed, and the write endpoint's retry safety is silently gone.

Follow-up

  • The fence lasts 90 seconds instead of 4 because the final delta keeps growing. What is happening, and what do you do while the tenant is fenced?
  • Two tenants must merge into one account. What does that cost under this scheme, and which step is not reversible?

Listing latency scales with page size, not with filters

Easy · n+1 · latency · query batching

The tenant listing endpoint reads resource filtered by tenant_id and status, ordered by updated_at DESC, and returns each row plus the owner's display name from app_user and the actor of that resource's latest resource_revision. p99 is 55 ms at 10 rows per page and 1.4 s at 200. Database telemetry shows 401 statements per request, each under 1 ms, and nothing in the slow-query log. Diagnose the cause and give the fix, stating the statement count per request and the p99 you expect afterwards.

Approach

  1. Read the counters before forming a theory. 401 statements for 200 rows is one driver query plus two per row, and sub-millisecond execution with an empty slow-query log rules out a bad plan. The time is round trips, which is why it is invisible in every per-query metric and scales with rows returned rather than with filter selectivity.
  2. Name the two per-row statements from their normalised text: a single-row app_user lookup by user_id, and a resource_revision lookup by resource_id ordered by version DESC LIMIT 1. Confirm by dropping those two response fields and watching the statement count fall to one. That locates the calls in the serialisation layer, not the repository.
  3. Check that the arithmetic accounts for the whole gap. Measure one round trip to the replica in isolation; 400 trips at roughly 3 ms of network plus 0.2 ms of execution is about 1.3 s on top of a 55 ms baseline, which matches. If the multiplication had fallen short, the N+1 would only be part of the story and you would keep looking.
  4. Batch both lookups. Collect owner_user_ids and resource_ids from the driver query, then issue WHERE tenant_id = $1 AND user_id = ANY($2) for the users, and PostgreSQL's SELECT DISTINCT ON (resource_id) ... WHERE resource_id = ANY($2) ORDER BY resource_id, version DESC for the latest revision, which the UNIQUE (resource_id, version) index serves directly. On an engine without DISTINCT ON, use a lateral join or a row_number window. Three statements per request at any page size.

Follow-up

  • The page size is capped at 200 today. What breaks first if it is raised to 2,000, and is it still this bug?
  • How do you stop the next N+1 from reaching production, given that no individual query is slow and the endpoint's tests pass?

Suggested practice checklist

Built from the rounds and topics The American Mathematical Society candidates report.

Day 1 — Map the The American Mathematical Society loop

  • Write out the reported sequence: Initial Assessment, Technical Interviews, Panel Discussions, Cultural Fit Conversations, Final Panel Interviews.
  • For each round, write one sentence on what it is judging, from the description above, and mark the one you are least ready for.

Deliverable: A one-page map of the 5 reported rounds, with the weakest marked.

Day 2 — Work Core Java

  • Spend the session on Core Java, which The American Mathematical Society candidates report being tested on.
  • Write one worked example in Core Java and time yourself on it.

Deliverable: One timed worked example in Core Java.

Day 3 — Work Java 8 (Java 1.8)

  • Spend the session on Java 8 (Java 1.8), which The American Mathematical Society candidates report being tested on.
  • Write one worked example in Java 8 (Java 1.8) and time yourself on it.

Deliverable: One timed worked example in Java 8 (Java 1.8).

Day 4 — Work Spring Boot

  • Spend the session on Spring Boot, which The American Mathematical Society candidates report being tested on.
  • Write one worked example in Spring Boot and time yourself on it.

Deliverable: One timed worked example in Spring Boot.

Day 5 — Answer out loud: Technical Competency and Language Proficiency

  • Answer aloud, timed: How would you describe your competency level in [Primary Language, e.g., Java]?
  • Answer aloud, timed: Can you explain the difference between specific features in Java 8 and later versions?

Deliverable: Spoken answers to 2 reported Technical Competency and Language Proficiency question(s), under time.

Day 6 — Answer out loud: Project Experience and Problem Solving

  • Answer aloud, timed: Can you walk through a past project that you found particularly challenging?
  • Answer aloud, timed: How do you approach the design of a software component from scratch?

Deliverable: Spoken answers to 2 reported Project Experience and Problem Solving question(s), under time.

Day 7 — Answer out loud: Behavioral and Career Alignment

  • Answer aloud, timed: Where do you see yourself in five years?
  • Answer aloud, timed: How do you handle collaborative environments, especially when working with non-technical stakeholders?

Deliverable: Spoken answers to 2 reported Behavioral and Career Alignment question(s), under time.

Behavioural preparation

Behavioural rounds judge the decision you made and what it cost.

What is your experience with modern web frameworks like Angular or backend frameworks like Spring Boot?

Medium · Technical Competency and Language Profic

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?

How do you handle debugging and performance optimization in a production environment?

Medium · Project Experience and Problem Solving

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?

Where do you see yourself in five years?

Medium · Behavioral and Career Alignment

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?

How do you handle collaborative environments, especially when working with non-technical stakeholders?

Medium · Behavioral and Career Alignment

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?

What attracts you to the mission of an organization like ours?

Medium · Behavioral and Career Alignment

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?

Describe a time you had to explain a technical concept to a non-technical team member.

Medium · Behavioral and Career Alignment

Approach

  1. Pick a story where you made the decision, not one where you watched it.
  2. State the situation in two sentences and spend the rest on the reasoning.
  3. Give the blast radius: what could have broken, and what you measured.
  4. Name the disagreement and how you resolved it with evidence.

Follow-up

  • What would you do differently if you ran that again?
  • How did you know your change caused the improvement?